Electro_Optics

Electro-Optics Handbook

Contents

Section

1 Radiometric Quantities and Units . . . . . . . . . . . . . .

1.1

1.2

1.3

1.4

Symbols, Names, and Units . . . . . . . . . . . .

Other Radiometric Definitions. . . . . . . . . . .

Radiation Conversion Chart . . . . . . . . . . . .

Electromagnetic Spectrum . . . . . . . . . . . . .

Page

9

9

12

13

13

2 Photometric Quantities, Units, and Standards. . . . . . . .

2.1

2.2

2.3

2.4

Symbols, Names, and Units . . . . . . . . . . . .

Photometric Standards . . . . . . . . . . . . . .

Illuminance, Luminous Exitance, and Luminance .

The Tungsten Lamp as a Luminous Intensity

Standard . . . . . . . . . . . . . . . . . . . . . .

15

15

15

17

19

3 Physical Constants, Angle Conversion Factors, and

Commonly Used Units . . . . . . . . . . . . . . . . . . .

3.1

3.2

3.3

3.4

Physical Constants . . . . . . . . . . . . . . . . .

Angle Conversion Factors . . . . . . . . . . . . .

Symbols and Definitions Commonly Used in

Electra-Optics . . . . . . . . . . . . . . . . . . .

Prefixes for Metric System Units. . . . . . . . . .

23

23

25

26

33

I

6

Section

Electro-Optics Handbook

Page

4

5

6

7

Blackbody Radiation . . . . . . . . . . . . . . . . . . . .

4.1

4.2

4.3

4.4

4.5

Equations . . . . . . . . . . . . . . . . . . . . .

Wavelength of Maximum Spectral Power

(Wien’s Displacement Law)

. . . . . . . . . . . .

Values of Constants in Radiation Equations . . . .

Blackbody Radiation Curves

. . . . . . . . . . .

Blackbody References . . . . . . . . . . . . . . .

35

35

Eye Response and Luminous Efficacy

. . . . . . . . . . .

5.1

5.2

5.3

5.4

5.5

5.6

Human Eye Response . . . . . . . . . . . . . . .

Thresholds of Human Eye Response . . . . . . . .

Color and the Human Eye . . . . . . . . . . . . .

Spectral Luminous Efficacy and Spectral

Luminous Efficiency

. . . . . . . . . . . . . . .

Luminous Efficacy and Luminous Efficiency . . .

Sample Calculations Involving Luminous

Efficacy . . . . . . . . . . . . . . . . . . . . . .

53

55

55

6.1

6.2

6.3

6.4

6.5

6.6

6.7

Source of Radiation. . . . . . . . . . . . . . . . . . . . .

61

The Sun . . . . . . . . . . . . . . . . . . . . . .

61

The Moon . . . . . . . . . . . . . . . . . . . . .

63

The Stars. . . . . . . . . . . . . . . . . . . . . . .

65

The Sky . . . . . . . . . . . . . . . . . . . . . .

68

Summary of Natural Illuminance Levels . . . . . .

72

Time Variation of Natural Illuminance

. . . . . .

72

Lamp Sources . . . . . . . . . . . . . . . . . . .

72

45

45

46

47

Atmospheric Transmittance . . . . . . . . . . . . . . . . .

7.1

7.2

7.3

7.4

7.5

7.6

7.7

Entire Atmosphere. . . . . . . . . . . . . . . . .

Horizontal-Path Transmittance. . . . . . . . . . .

Horizontal Visibility . . . . . . . . . . . . . . . .

Calculation of Atmospheric Transmittance in the 0.4-µm to 4-µm Region

. . . . . . . . . . . .

Calculation of Atmospheric Transmittance in the 8-µm to 14-µm Infrared Region . . . . . . . .

Effects of Atmosphere on Imaging Sensor

Performance . . . . . . . . . . . . . . . . . . . .

Atmospheric Backscatter - Artificial

Illumination . . . . . . . . . . . . . . . . . . . .

81

82

82

87

87

91

93

97

36

37

37

42

Contents

Section

7

Page

8

9

10

11

Detection, Resolution, and Recognition. . . . . . . . . . .

109

8.1

8.2

8.3

8.4

8.5

Pulse Detection in White Noise. . . . . . . . . . .

Pulse Detection in Quantum Noise . . . . . . . . . .

MTF (Modulation Transfer Function) and CTF

109

113

(Contrast Transfer Function) . . . . . . . . . . .

114

Display Interpretation . . . . . . . . . . . . . . .

119

Target Detection/Recognition Model. . . . . . . .

121

9.1

9.2

9.3

9.4

9.5

Lasers .

9.6

9.6a

9.6b

...........................

127

Crystalline Lasers . . . . . . . . . . . . . . . . .

128

Glass Lasers . . . . . . . . . . . . . . . . . . . .

128

Gas Lasers . . . . . . . . . . . . . . . . . . . . .

128

Dye Lasers . . . . . . . . . . . . . . . . . . . . .

132

Second Harmonic Generation and Parametric

Down-Conversion . . . . . . . . . . . . . . . . .

133

P-N Junction Light Sources . . . . . . . . . . . .

135

P-N Junction Lasers . . . . . . . . . . . . . . . .

139

Light-Emitting Diodes (LED’s). . . . . . . . . . .

145

Detector Characteristics . . . . . . . . . . . . . . . . . . . 146

10.1

10.2

10.3

10.4

10.5

Fundamental Photodetector Relationships and Definitions . . . . . . . . . . . . . . . . . .

146

Spectral Responsivity and Specific Spectral

Detectivity . . . . . . . . . . . . . . . . . . . . . 15 1

Noise . . . . . . . . . . . . . . . . . . . . . . . 160

Time Characteristics of Photodetectors . . . . . 167

Source-Detector Matching . . . . . . . . . . . . . 170

11.1

11.2

11.3

11.4

11.5

11.6

11.7

Image and Camera Tubes . . . . . . . . . . . . . . . . . .

173

11.8

11.9

Image Tubes. . . . . . . . . . . . . . . . . . . .

173

Characteristics of Image Tubes. . . . . . . . . . .

176

Television Camera Tubes. . . . . . . . . . . . . .

180

Responsivity

. . . . . . . . . . . . . . . . . . .

185

Signal-to-Noise Ratio. . . . . . . . . . . . . . . .

190

Lag

. . . . . . . . . . . . . . . . . . . . . . . .

191

Modulation Transfer Function and Contrast

Transfer Function . . . . . . . . . . . . . . . . .

193

Limitations to Low-Light-Level Viewing. . . . . .

195

Recognition Statistics . . . . . . . . . . . . . . .

196

8

Section

12

Electro-Optics Handbook

Page

11.10

Lens and Sensor Limitations . . . . . . . . . . . . 199

11.11

Practical Detection and Recognition Parameters . . 202

12.1

12.2

12.3

12.4

12.5

12.6

12.7

12.8

12.9

Optics. . . . . . . . . . . . . . . . . . . . . . . . . . . . 209

Thin-Lens Characteristics and Formulae . . . . . .

209

Thick-Lens Characteristics . . . . . . . . . . . . .

212

Lens Aberrations. . . . . . . . . . . . . . . . . .

2 12

MTF Characteristics of Lenses . . . . . . . . . . .

213

Diffraction Limits . . . . . . . . . . . . . . . . .

214

Illuminance and Irradiance Formulae. . . . . . . .

2 16

Properties of Optical Glasses . . . . . . . . . . . .

217

Spectral Transmittance of Materials . . . . . . . .

2 17

Corner Reflectors . . . . . . . . . . . . . . . . .

2 17

13 Photographing E-O Displays . . . . . . . . . . . . . . . . 225

13.1

13.2

13.3

13.4

Sensitometry . . . . . . . . . . . . . . . . . . . . 225

Film Selection for Cathode-Ray Tube Recording. .

233

Photographing Cathode-Ray Tube Images . . . . .

236

Lens-Aperture and Exposure-Meter-Setting

Formulae. . . . . . . , . . . . . . . . . . . . . . 236

14 Contributors . . , . . . . . . . . . , . . . . . . . . . . . 241

Index . . . . . , . . . , . . . . . . . . . . . . . . . . . . 243

Section 1

Radiometric Quantities and Units

1.1 SYMBOLS, NAMES, AND UNITS

Figure l-l gives the standard quantities of physical measurements which are basic to the definitions of the radiometric and photometric terms given in this

Handbook.

Quantity Symbol SI unit Symbol

Length l, r, s meter m

Area A square meter m2

Volume V cubic meter m3

Solid Angle steradian sr

Frequency hertz Hz

Wavelength meter m

Time t second S

Fig. 1-1 Basic quantities of physical measurements.

Figures 1-2 and 1-3 summarize the basic radiometric and spectroradiometric quantities, definitions, units, and symbols. In accord with current international standardization, in these figures only the International System of

Units (SI units) are shown. Their counterparts in other systems are shown in

Figures 2-2, 2-3, 2-4, and 3-3.

9

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1 0 Electro-Optics Handbook

The units for wavelength deserve special mention. In all of the figures, the as Planck’s spectral radiation formula, wavelength is given in meters.

Quantity

Radiant energy

Symbol

Defining Equation* SI

Unit

Symbol

Radiant density

W, We joule joule per cubic meter watt Radiant flux

Radiant flux density at a surface :

Radiant exitance

(Radiant emittance)

Irradiance

Radiant intensity

M,Me

E, Ee watt per square meter watt per square meter watt per steradian

W which flux from point source is radiated)

Radiance

L, Le watt per steradian and square meter sight and normal to emitting surface considered)

*

Note: The symbols for photometric quantities (Section 2) are the same as those for corresponding radiometric quantities. When it is necessary to differentiate between the two quantities, the subscripts v

Table adapted from U.S.A. Standard Letter Symbols for Illuminating Engineering (USAS Y 10.18-1967) published by the

American Society of Mechanical Engineers, United Engineering Center, 345 East 47th Street, New York, New York 10017.

Fig. 1-2 Radiometric quantities and units.

12

Electro-Optics Handbook

1.2 OTHER RADIOMETRIC DEFINITIONS (See Figure 1-4)

Reflectance

Emissivity l

Radiant absorptance should not be confused with absorption coefficient (mentioned in Section 7.2).

Fig. 1-4. Other radiometric quantities and units.

The processes of absorption, reflection (including scattering), and transmission account for all incident radiation in any particular situation, and the absorptance, reflectance, and transmittance must add up to one:

(1-1)

(1-2)

A Lambertian surface is a perfectly diffuse surface which has a constant radiance L independent of viewing direction; constant radiance is given by the formula

Radiometric Quantities and Units 13

where the units of L are W m

-2 sr

-1 and the units of M the radiant exitance are W m

-2

1.3 RADIATION CONVERSION CHART

Figure 1-5 presents a useful nomograph for quick conversion of radiation quantities. Note that the µm scale appears at both margins to permit aligning a straight edge across the other scales.

ULTRA

VIOLET

VISIBLE

INFRARED

Fig. 1-5 Radiation conversion chart (Adapted from Reference 1).

1.4 ELECTROMAGNETIC SPECTRUM

Figure l-6 shows the entire electromagnetic spectrum for wavelengths from

1 0

-10

µm to 10

5 km. The UV, visible, and IR portion has been separately expanded for greater definition.

Reference

1. Blattner, D., “Radiation Nomograph,” ELECTRONIC DESIGN, Vol. 14,

No. 22, Sept. 27, 1966

14

WAVELENGTH

LONG ELECTRICAL

OSCILLATIONS

Electro-Optics Handbook

WAVELENGTH

1 KILOMETER (km)

RADIO

WAVES

MICROWAVES

1 CENTIMETER (cm)

-1 MILLIMETER (mm)

492

-

Fig. 1-6 Electromagnetic spectrum.

Back

15

Section 2

Photometric Quantities, Units, and Standards

2.1 SYMBOLS, NAMES, AND UNITS

Figure 2-1 summarizes the basic photometric quantities, definitions, units, and symbols. This table parallels that of Figure 1-2.

2.2 PHOTOMETRIC STANDARDS

The candela-The standard candle has been redefined as the new candle or candela (cd). One candela is the luminous intensity of 1/60 of 1 cm2 of the projected area of a black body radiator operating at the temperature of the solidification of platinum (2045 K). The candela emits one lumen per steradian (1 lm sr

-1

).

Note that the luminous intensity emanating from a source with a spectral distribution that differs from that of the standard candle may be evaluated by using a sensor whose relative spectral response is identical to that standardized for photopic vision. See Section 5.

The lumen-The lumen (lm) is defined in terms of the candela. The luminous flux per steradian from a source whose luminous intensity is 1 candela is 1 lumen.

16 Electro-Optics Handbook

Quantity Symbol

Luminous energy

(quantity of light)

Q, Q v

Luminous density w, w v

Luminous flux

Luminous flux density at a surface

Luminous exitance

(formerly luminous emittance)

Illuminance

(formerly illumination)

Luminous intensity

(formerly candlepower)

M, M v

SI Unit Symbol

lumen second

(talbot) lm s lumen second per cubic meter lumen lm s m l m

-3 lumen per square meter lux (lumen per square meter) lm m lx

-2 candela

(lumen per steradian) cd

Luminance

(formerly photometric brightness)

L, L v nit

(candela per square meter or lumen per steradian and square meter) nt luminous efficacy

K lumen per watt lm W

-1 spectral luminous efficacy lumen per watt lm W

Luminous efficiency (numeric)

-1

Note: The symbols for photometric quantities are the same as those for corresponding radiometric quantities, shown in Section 1. When it is necessary to differentiate between the two quantities, the subscripts v should be used for photometric quantities and e for radiometric quantities, e.g., Q, and Q e

.

Street, New York, New York 10017.

Fig. 2-l Photometric quantities and units.

Photometric Quantities, Units, and Standards

2.3 ILLUMINANCE, LUMINOUS EXITANCE, AND LUMINANCE

17

A schematic representation depicting the relationships of commonly employed photometric units is shown in Figure 2.2.

X represents point source having a linear intensity of one candela. Solid angle shown represents one steradian.

Point “X” to any point “B” is 1 cm; the surface represented by “BBBB” is

1 cm

2

.

Point “X” to any point “C” is 1 ft; the surface represented by “CCCC” is 1 ft2.

Point “X” to any point “D” is 1 m; the surface represented by “DDDD” is

1 m2.

Fig. 2-2 Schematic representation of various photometric units (Courtesy of

National Bureau of Standards).

illumination. (Note the distinction that dA in the definition for E is the

(SI unit) is the unit of illuminance resulting from the flux of 1 lumen falling on the surface represented by “DDDD” from “X” = 1 candela.

18

Electro-Optics Handbook

The footcandle is the unit of illuminance resulting from the flux of 1 lumen falling on the surface represented by “CCCC” from “X” = 1 candela. The phot is the unit of illuminance resulting from the flux of 1 lumen falling on the surface represented by “BBBB” from “X” =

1

candela.

Conversion factors for these units are shown in Figure 2-3.

footcandle phot

(fc) (ph)

= 1 0.0929 1 x 10

-4

1 lux (lm m

-2

)

(lx)

1 footcandle (lm f t

- 2

)

(fc)

1 phot (lm cm

-2

)

( p h )

= 10.764 1 0.001076

= 1 x 1 0

4

929 1

Fig. 2-3 Conversion factors for commonly used illuminance quantities

per unit surface area. It applies for either self-luminous or reflective bodies.

Referring to Figure 2-2 and assuming 100% of the luminous flux from “X” (1 candela in all directions) is reflected by surfaces represented by “DDDD”,

“CCCC”, or “BBBB”, then:

1. “DDDD” will have an exitance of 1 lumen/m

2

2. “CCCC” will have an exitance of 1 lumen/ft

2

3. “BBBB” will have an exitance of 1 lumen/cm2

Figure 2-4 gives conversion factors for commonly used luminous exitance quantities.

the luminous intensity per projected area normal to the line of observation.

Referring to Figure 2-2 and assuming 100% of the luminous flux from “X” (1 candela in all directions) is reflected in a perfectly diffuse manner (Lambert’s

Cosine Law) by the surface represented by “DDDD”, “CCCC”, or “BBBB”, then:

Photometric Quantities, Units, and Standards

19

1. “DDDD” will have a directionally uniform luminance of 1 apostilb or

2. “CCCC” will have a directionally uniform luminance of 1 footlambert or

3. “BBBB” will have a directionally uniform luminance of 1 lambert or

1 lm m

-2

1 lm ft

-2

1 lm cm

-2

=

=

=

1

10.764

1 x 10

4

0.0929

1

929

1 x 10

-4

0.001076

1

Fig. 2-4 Conversion factors for commonly used luminous exitance quantities.

unit area and unit solid angle from a Lambertian emitter over a solid angle of where M is the exitance in lm m

-2 and L is the luminance in lm sr

-1 m

-2

.

Figure 2-5 gives conversion factors for commonly used luminance units.

2.4 THE TUNGSTEN LAMP AS A LUMINOUS INTENSITY STANDARD

Although the candela is defined in terms of a blackbody at 2045 K, use of such a source is inconvenient in most laboratories. In the electro-optic industry, the tungsten-filament light source or lamp is commonly employed to evaluate electro-optic devices. These lamps are calibrated for candlepower and are maintained at a standard color temperature, usually 2856 K. Even though the spectral distribution of radiation from such a tungsten source differs considerably from that of a blackbody at 2045 K, this source has the practical advantages of being simple to operate and calibrate, is relatively stable, and provides radiation over a broad spectral band.

Photometric Quantities, Units, and Standards 21

If a source such as a tungsten lamp is to be rated against the standard blackbody source, it is important that the sensor used in the comparison have a spectral response closely equivalent to that of the standard photopic eye.

Otherwise, significant errors could result because of radiation differences outside the visible range. When such a standard tungsten lamp is used to rate the responsivity of a detector, it must be understood that the luminous rating of the lamp is only a measure of its radiance in the visible region. A major part of the radiation from a tungsten lamp is actually in the infrared region.

Misinterpretation can result from the quoting of luminous responsivity of a sensor, particularly if the sensor has infrared sensitivity. Photometers with characteristics comparable to the human eye are available from many manufacturers.

A preferred method of specifying sensor responsivities which avoids all ambiguities is to provide spectral radiant measurements over the entire spectral range of the sensor. From these measurements, luminous responsivities can be calculated for sources of any color distribution. Because radiant measurements require elaborate equipment and are time consuming, most photosensor manufacturers take 100% luminous responsivity measurements and make only spot measurements of spectral response. Even if the responsivities are defined in terms of total incident flux from the source in watts instead of lumens, the ambiguity resulting from different possible spectral radiation distributions still exists, although the inconsistency of rating an infrared sensitive sensor in terms of luminous responsivity is eliminated.

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23

Section 3

Physical Constants, Angle Conversion

Factors, and Commonly Used Unit

Symbols

3.1 PHYSICAL CONSTANTS

Figure 3-1 lists some useful physical constants often encountered in electrooptics.

3.2 ANGLE CONVERSION FACTORS

Figure 3-2 provides a table of angle conversion factors.

3.3 SYMBOLS AND DEFINITIONS COMMONLY USED IN ELECTRO-

OPTICS

Figure 3-3 lists the symbols and definitions for the units most commonly encountered in radiometry and photometry. This Figure, as well as Figure 3-4 is adapted from American National Standard Letter Symbols for Units Used in

Science and Technology, (ANSI Y 10.19-1969), with the permission of the publisher, The American Society of Mechanical Engineers, United Engineering

Center, 345 East 47th Street, New York, New York 10017.

3.4 PREFIXES AND METRIC SYSTEM UNITS

Figure 3-4 gives the multiplying prefixes and associated symbols for metric units.

24 Electro-Optics Handbook

References

2. Taylor, B.N., Parker, W.H., and Langenberg, D.N., “Determination of e/h, Using Macroscopic Quantum Phase Coherence in Superconductors:

Implications for Quantum Electrodynamics and the Fundamental Physical

Constants,” REVIEW OF MODERN PHYSICS, Vol. 41, No. 3, July 1969.

Physical constant

Avogadro’s number

Boltzmann’s constant

Electron charge

Electron charge to mass ratio

Energy of 1 electron volt

Voltage-wavelength conversion factor kT value at room temperature

Luminous efficacy at 555 nm

Mass of electron in free space

Permittivity of free space

Planck’s constant

Second radiation constant (hc/k)

Speed of light in vacuum

Stefan-Boltzmann constant

Symbol Value Unit

N 6.022169 x 10 23 mol

-1 k 1 . 3 8 0 6 2 2 x 1 0

-23

J K

- 1 e 1.6021917 x 10

-19

C e/m 1.7588028 x 10

11

C kg

-1 eV 1.6021917 x 10 -19

J hc/e 1.2398541 x 10

-6

V m

C

1

4 . 9 9 2 5 7 9 x 1 0

-24

J m

0.0259

eV

673 lm W

-1 m 9.109558 x 10

-31 k g

8.86 x 10

-12

F m

-1 h 6 . 6 2 6 1 9 6 x 1 0

-34

J s

C

2

C

0.01438833

2.9979250 x 10

8 mK m s

-1

5.66961 x 10

-8

W m -2

K

- 4

Fig. 3-I Useful physical constants (Adapted from Reference 2).

Physical Constants, Angle Conversion Factors, and Unit Symbols 25

bel bit

26

Unit

ampere ampere (turn) ampere per meter angstrom apostilb atmosphere, standard atomic mass unit (unified) bar barn baud

Electro-Optics Handbook

A

A

Symbol Notes

SI unit of electric current

SI unit of magnetomotive force

A/m

SI unit of magnetic field strength asb atm

U bar b

Bd

B

b

A unit of luminance. One lumen per square meter leaves a surface whose luminance is one apostilb in all directions within a hemisphere. Use of the SI unit of luminance, the candela per square meter, is preferred.

1 atm = 101,325 N m-2

The (unified) atomic mass unit is defined as one-twelfth of the mass of an atom of the

12

C nuclide. Use of the old atomic mass

(amu), defined by reference to oxygen, is deprecated.

1 bar = 100,000 N m-2

b = 10-28 m

2

In telecommunications, a unit of signaling speed equal to one element per second.

The signaling speed in bauds is equal to the reciprocal of the signal element length is seconds.

A dimensionless unit for expressing the ratio of two values of power, the number of bels being the logarithm to the base 10 of the power ratio.

A unit of information. The capacity in bits of a storage device is expressed as the logarithm to the base two of the number of possible states of the device.

Fig. 3-3 Units commonly used in radiometry and photometry.

Part 1 of 7

Physical

Constants,

Angle Conversion Factors, and Unit Symbols 27 unit

Symbol

bit per second b/s calorie (International Table calorie) c a l

I T calorie (thermochemical calorie) candela candela per square meter candle cal cd cd/m2 cd

Notes

1 cal

IT

= 4.1868J

The 9th Conference Generale des Poids et

Mesures adopted the joule as the unit of heat. Use of the joule is preferred.

1 cal = 4.1840 J (See note for International

Table calorie.)

SI unit of luminous intensity

SI unit of luminance. The name nit is sometimes used for this unit.

The unit of luminous intensity has been given the name candela; use of the name candle for this unit is deprecated.

circular mil coulomb curie cmil

C

Ci cycle per second

Hz dB

SI unit of electronic charge

1 Ci = 3.7 x 10

10 disintegrations per second. Unit of activity in the field of radiation dosimetry.

See Hertz. The name hertz is internationally accepted for this unit; the symbol Hz is preferred to c/s.

One tenth of a be1 decibel degree (temperature) degree Celsius degree Fahrenheit

°C

°F

The use of the word centigrade for the

Celsius temperature scale was abandoned by the Conference Generale des Poids et

Mesures in 1948. Note there is no space between the symbol ° and the letter.

See kelvin degree Kelvin degree Rankine dyne electronvolt

K

°R dyn eV

The CGS unit of force

The energy received by an electron in falling through a potential difference of one volt.

Fig. 3-3 Units commonly used in radiometry and photometry.

Part 2 of 7

28

farad foot footcandle footlambert gilbert gram henry hertz inch joule joule per kelvin kelvin

Unit

Electro-Optics Handbook

in

J

J/K

K g

H

Hz

F ft fc

Symbol

Notes

The unit of energy in the CGS system of units

SI unit of capacitance fc = lm ft

-2

The name lumen per square foot is recommended for this unit. Use of the SI unit of illuminance, the lux (lumen per square meter), is preferred.

fL

G

Gb

A unit of luminance. Use of the SI unit, the candela per square meter, is preferred.

The gauss is the electromagnetic CGS unit of magnetic flux density. Use of SI unit, the tesla, is preferred.

The gilbert is the electromagnetic CGS unit of magnetomotive force. Use of the

SI unit, the ampere (or ampere turn), is preferred.

SI unit of inductance

SI unit of frequency

SI unit of energy

SI unit of heat capacity and entropy

In 1967 the CGPM gave the name kelvin to the SI unit of temperature which had formerly been called degree Kelvin and assigned it the symbol K (without the symbol °).

SI unit of mass

Fig. 3-3 Units commonly used in radiometry and photometry.

Part 3 of 7

Physical Constants, Angle Conversion Factors, and Unit Symbols 29

kilogram-force

Unit

knot lambert liter lumen lumen per square foot lumen per square meter lumen per watt lumen second lux maxwell meter mho micrometer micron kn

L kgf

1 lm lm/ft

2 lm/m

2 lm/W lm s lx

M x m mho

Notes

In some countries the name kilopond (kp) has been adopted for this unit.

kn = nmi hr

-1

-2

A CGS unit of luminance. Use of the SI unit of luminance, the candela per square meter, is preferred.

11= 10

-3 m3

SI unit of luminous flux

A unit of illuminance and also a unit of luminous exitance. Use of the SI unit, lumen per square meter, is preferred.

SI unit of luminous exitance.

SI unit of luminous efficacy.

SI unit of quantity of light, also known as the talbot.

lx = lm m

-2

SI unit of illuminance

The maxwell is the electromagnetic CGS unit of magnetic flux. Use of the SI unit, the weber, is preferred.

SI unit of length

CIPM has accepted the name siemens (S) for this unit and will submit it to the 14th

CGPM for approval.

µm

µm

See micrometer. The name micron was abrogated by the Conference Generale des

Poids et Mesures, 1967.

Fig. 3-3 Units commonly used in radiometry and photometry.

Part 4 of 7

30

Electro-Optics Handbook

mi1 mile (statute) mile per hour millimeter conventional millimeter of mercury millimicron minute (time) mole nautical mile neper newton newton meter newton per square meter newton second per square meter nit oersted ohm

Symbol

mil mi mi/h

Notes

1 mil = 0.001 in

1 mi = 5280 ft

Although use of mph as an abbreviation is common, it should not be used as a symbol.

mm mmHg nm

1 mmHg = 133.322 N m

-2

Use of the name millimicron for the nanometer is deprecated.

min mol nmi

Np

Time may also be designated by means of superscripts as in the following example,

9h 46m 30s.

SI unit of amount of substance.

1 nmi = 1852 m

The natural logarithm of the scalar ratio of two currents or voltages.

SI unit of force N

N m

N/m

2

Unit of energy equal to one joule.

SI unit of pressure or stress. See pascal

N s / m

2

SI unit of dynamic viscosity nt nt = cd m

-2

The name nit is given to the SI unit of luminance, the candela per square meter.

Oe The oersted is the electromagnetic CGS unit of magnetic field strength. Use of the SI unit, the ampere per meter, is preferred.

SI unit of resistance

Fig. 3-3 Units commonly used in radiometry and photometry.

Part 5 of 7

Physical Constants, Angle Conversion Factors, and Unit Symbols 31

Unit

ounce (avoirdupois) pascal phot poise rad radian rem roentgen second (time) siemens steradian stilb stokes

S

S

Symbol

oz

Pa ph

P rd rad rem

R

Notes

Pa = N m

-2

SI unit of pressure or stress. This name accepted by the CIPM in 1969 for submission to the 14th CGPM.

ph = lm cm

-2

CGS unit of illuminance. Use of the SI unit, the lux (lumen per square meter), is preferred.

P = dyn s cm

-2

Unit of coefficient of viscosity.

Unit of absorbed dose in the field of radiation dosimetry.

SI unit of plane angle

Unit of dose equivalent in the field of radiation dosimetry.

Unit of exposure in the field of radiation dosimetry.

SI unit of time sr sb

SI unit of conductance. This name and symbol were accepted by the CIPM in

1969 for submission to the 14th CGPM.

The name mho is also used for this unit in the USA.

SI unit of solid angle sb = cd cm

-2

A CGS unit of luminance. Use of the SI unit, the candela per square meter, is preferred.

St Unit of viscosity

-

Fig. 3-3 Units commonly used in radiometry and photometry

Part 6 of 7

32

Electro-Optics Handbook

tesla tonne var volt volt per meter voltampere

Unit

t

Symbol

T

Notes

T = N A

-1 m-l = Wb m

-2

SI unit of magnetic flux density (magnetic induction) var

V

1 t= 1000 kg

IEC name and symbol for the SI unit of reactive power

SI unit of voltage

V/m

VA

SI unit of electric field strength

IEC name and symbol for the SI unit of apparent power

W SI unit of power

W/(m.K) SI unit of thermal conductivity watt watt per meter kelvin watt per steradian W/sr SI unit of radiant intensity watt per steradian and square meter W/(sr.m

-2

) SI unit of radiance watthour Wh weber Wb W b = V s

SI unit of magnetic flux

CGPM Conference Generale des Poids et Mesures (General Conference on Weights and

Measures)

CGS Centimeter-Gram-Second

CIPM Comite International des Poids et Mesures (International Committee for Weights

IEC

MKS

SI and Measures)

International Electrotechnical Commission

Meter-Kilogram-Second

Systeme International d’Unites (International System of Units)

Fig. 3-3 Units commonly used in radiometry and photometry.

Part 7 of 7

Physical Constants, Angle Conversion Factors, and Unit Symbols 33

Prefix (Multiple)

Symbol

tera (10

1 2

) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T giga (10

9

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . G mega (10

6

) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . M kilo (10

3

) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . k hecto (10

2

) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . h deka (10) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . da deci (10

-1

) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . d centi (10

-2

) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . c milli (10

-3

)

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . m micro (10

-6

) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . µ nano (10

-9

) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . n pico (10

-12

) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . p femto (10

-15

) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

f atto (10

-18

) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . a

-

Fig. 3-4 Metric unit prefixes and symbols.

Back

35

Section 4

Blackbody Radiation

4.1 EQUATIONS*

The equation for spectral radiant exitance (Planck’s) is

(4-1) where wavelength (m) h = Planck’s constant (J s)

C

= velocity of light in a vacuum (m s

-1

) k = Boltzmann’s constant (J K

-1

)

T = absolute temperature (K) according to equation 1-3 because blackbodies are Lambertian sources; hence,

(4-2)

*See Section 1 for further definition of symbols.

36

Electro-Optics Handbook

Equation 4-2 gives the spectral radiance per unit of wavelength increment.

A useful alternative to equation 4-2 gives the spectral radiance in number of quency);

Another useful alternative is the expression,

(4-4) which gives the spectral radiance per frequency increment.

(4-5)

Radiant exitance, M, is given by the Stefan-Boltzmann equation:

(4-6)

(4-7)

4.2 WAVELENGTH OF MAXIMUM SPECTRAL POWER (WIEN’S DIS-

PLACEMENT LAW)

It can be shown from equations 4-1 and 4-2 that blackbodies at temperature mined from

Blackbody Radiation

or

37

(4-8)

The number of photons per second, however, based on equation 4-3, is or

4.3 VALUES OF CONSTANTS IN RADIATION EQUATIONS

3.7418 x 10

-16

W m2

2c2h = 1.1911 x 10

-16

W m2 sr

-1

2c = 5.9958 x 10

8 photons sr

-1 m s

-1

2h/c2

= 1.4745 x 10

-50

W H

Z

-4 m

-2 s r

-1 ch/k =

0.014388 m K c, h, k (See Figure 3-1)

4.4 BLACKBODY RADIATION CURVES

Figure 4-l

Figure 4-2

Electro-Optics Handbook

Fig.

shown on each curve. The diagonal line intersecting the curves at their maxima shows Wien's displacement law. Subdivisions of the ordinate scale are at 2 and 5. (Adapted from Reference 8 with permission).

Fig

Black body Radiation

Fig. 4-2 Number of photons per second emitted per square meter per steradian per micrometer by a blackbody at various absolute temperatures. The diagonal line intersecting the curves at their maxima shows Wien's displacement law. (Adapted from Reference 8 with permission).

Figure 4-4 - The fraction of total blackbody radiant exitance that is luminous (i.e., visible) as a function of absolute temperature

T. See Section 5.5

Figure 4-5 absolute temperature T from 250 K to 500 K.

Figure 4-6

Spectral-band radiance contrast for the spectral bands 8-14

µm, 8-13 µm, and 8-11.5 µm.

Electro-Optics Handbook

Fig. 4-3 Blackbody functions of AT: (1) Ratio of spectral exitance or

Electro-Optics Handbook

Fig. 4-3 Blackbody functions of

λΤ:

Blackbody Radiation

41

the average human eye (Adapted from Fig. 11-15 of Reference 7 with permission).

42

Electro-Optics Handbook

temperature T shown on each curve (Plotted from tables in part 5 of

Reference 9).

4.5 BLACKBODY REFERENCES

Theory,

Radiation Slide Rules - Reference 3, Chapter 2

Theory - Reference 4

Blackbody Radiation

Tables - Reference 5

Reference 6, Section 6k

(page 6-153)

Curves - Reference 7, pages 43 - 57

Reference 8, Appendix B

43

ABSOLUTE TEMPERATURE (T)-K

Fig. 4-6 Spectral-band radiance contrast for three spectral bands as a function of absolute temperature (Plotted from tables in part 5 of

Reference 9).

References

3. Wolf, W.L., Editor, HANDBOOK OF MILITARY INFRARED TECH-

NOLOGY, Office of Naval Research, Dept. of the Navy, Washington, D.C.,

1965.

44

Electro-Optics Handbook

4. Merritt, T.P. and Hall, F.F. Jr., “Blackbody Radiation,” PROC. IRE, Sept.

1959.

5. Pivovonsky, M. and Nagel, M., TABLES OF BLACKBODY RADIATION

FUNCTIONS, Macmillan, New York, N.Y., 1961

6. AMERICAN INSTITUTE OF PHYSICS HANDBOOK, Second edition,

McGraw-Hill Book Co., Inc. New York, N.Y., 1962.

7. Mauro, J.A., Editor, OPTICAL ENGINEERING HANDBOOK, General

Electric Co., Syracuse, N.Y., 1966.

8. Valley, S.L., HANDBOOK OF GEOPHYSICS AND SPACE ENVIRON-

MENTS, Air Force Cambridge Research Laboratories, Office of Aerospace

Research. U.S. Air Force, 1965. Also published by McGraw-Hill Book Co.,

New York, N.Y., 1965.

9. Bramson, M.A., INFRARED RADIATION, A HANDBOOK FOR

APPLICATIONS, Plenum Press, New York, N.Y., 1968.

Back

45

Section 5

Eye Response and

Luminous Efficacy

5.1 HUMAN EYE RESPONSE

Receptors of the Human Eye-The human eye contains two types of retinal

receptors, rods and cones.

Photopic Eye Response (Cone Vision) - Photopic response is that of the cones

in the retina and occurs after the eye has been adapted to a field luminance equal to or greater than about 3 nt (cd m

-2

) (light-adapted state). After being dark adapted, the eye requires ‘about two or three minutes to become light adapted when the luminance is raised.

Scotopic Eye Response (Rod Vision) - Scotopic response is that of the rods in

the retina and occurs after the eye has been adapted to field luminance equal to, or less than, about 3 x 10

-5 nt (cd m

-2

). After being light adapted, the eye requires considerable time to become dark adapted when the luminance is lowered. See Figure 5-l. The rate of adaption depends on the initial luminance of the starting field with nearly complete dark adaption being approached in about 45 minutes. See Reference 10. Because the rods and not the cones function in the dark-adapted state and because color vision is entirely a function of the cones, the increased responsivity of the eye in the dark-adapted state is accompanied by a loss in color vision. The central part of the retina known as the fovea contains only cones.

46 Electro-Optics Handbook

TIME IN THE DARK-MINUTES

Fig. 5-1 Adaption of the eye to complete darkness after exposure to a bright field. Light incident 12° above fovea. (Adapted from Wald et al,

Reference 10, with permission).

The spectral responsivity of the eye in the dark-adapted (scotopic) state differs considerably from the light-adapted (photopic) state. Between these two states, the spectral response of the eye is continuously variable; this condition is known as the mesopic state.

Mesopic Eye Response-As field luminance is lowered from about 3 nt to 3 x

10

-5 nt (cd m

-2

), the luminous efficacy curve of the eye shifts progressively from that of photopic vision to that of scotopic vision. See Reference 11, pp

5 through 8. Table II of this reference gives mesopic values of relative luminous efficacy corresponding to nine different values of luminance between the photopic and scotopic states.

5.2 THRESHOLDS OF HUMAN EYE RESPONSE

Hecht, Schlaer and Pirenne (1942) established that the minimum detectable visual stimulus is produced by 58 to 145 quanta of blue-green light (510 nm) impinging on the cornea. This stimulus, it was estimated, provides only from

5 to 14 quanta actually reaching and acting on the retinal sensors (see page

154 of Reference 12).

Experimental determinations have been made by Blackwell (1946) of the minimum contrast (L o

-Lb)/Lb of an object with luminance L, against a background with luminance Lb for a 50% probability of detection when both eyes are used and when unlimited time of exposure is available (Reference

Eye Response and Luminous Efficacy

47

13). The results are given in Figure 5-2. Note the discontinuity in all the curves on Figure 5-2 at about 2 x 10

-3 nt (cd m

-2

). This point marks the transition from photopic to scotopic vision.

Figure 5-3 gives the threshold illuminance Et at the eye produced by a fixed barely detectable achromatic point source against a background luminance Lb as determined experimentally by a number of observers. The Tiffany data are for a 50% probability of detection; the other curves are for a practical certainty of detection. For convenient reference, an illuminance scale is also given in units of stellar magnitude (defined in Section 6). The discontinuity between photopic and scotopic vision is again evident on the curves.

Studies have been made by Griffin, Hubbard, and Wald to determine the spectral characteristics of the fully dark-adapted eye. See Reference 15.

Figure 5-4 is a composite spectral response characteristic for the dark-adapted fovea and the peripheral retina based on the referenced work and on data from previous work. Because only the rods function in the dark-adapted state, faint signals are seen better in darkness when viewed indirectly. This characteristic is particularly true at the extremities of the visual spectral range.

5.3 COLOR AND THE HUMAN EYE

Trichromatic Response Theory of the Human Eye-The exact mechanics of human color vision are unknown but it has been determined that the response is shared by the eye and the brain.

Fig. 5-2 Thresholds of brightness contrast for 50% probability

of

detection of objects brighter than their backgrounds. Unlimited exposure time

(Adapted from Blackwell, Reference 13, with permission).

48

10-3

Electro-Optics Handbook

Fig. 5-3 Threshold illuminance for human eye from a fixed achromatic point source as a function of background luminance (Adapted from

Middleton, Reference 14, with permission).

The trichromatic theory holds that the retina of the eye consists of a mosaic of three different receptor elements. Each element responds to specific wavelengths corresponding to blue, green, and red light. These three elements, which appear to overlap considerably in responsivity, are separately connected through nerves to the brain where the sensation of color is derived by the brain’s analysis of the relative stimulus from the three elements.

Color is perceived as a conscious sensation in terms of three major subjective attributes, luminance, hue, and saturation; primary among these attributes is luminance (often called brightness). The second major attribute, hue, which is the most characteristic of color, is the distinction between redness, yellowness, blueness, etc. The hue of pure colors of the physical spectrum, relates directly to wavelength. The third attribute, which distinguishes strong colors from pale ones, is saturation or chroma. Saturation is related to physical purity, i.e., freedom from dilution by white.

Although the eye is not suitable for measuring color directly, it is a highly efficient color-matching instrument. This property of vision is utilized in calorimetry in which any color stimulus may be specified by finding a known

Eye Response and Luminous Efficacy

49

Fig. 5-4 Relative spectral responsivity of the dark-adapted fovea and peripheral retina (Adapted from Griffin et al, Reference 15, with permission).

second stimulus that the eye establishes as equivalent. In modern calorimetry, the second stimulus is usually a combination of red, green, and blue light; however, any three monochromatic (single color) colors can be used as primaries providing no two colors can be mixed in any proportion to match the third color.

50

Electro-Optics Handbook

Standard Color-Mixture Curves-Most color sensations can be matched by the mixture of three primary colors in suitable quantities. The three primaries may be but are not necessarily monochromatic. Typical primaries may be red, green, and blue. In using such a set of colors for matching, it may be necessary sometimes to use negative amounts of one of the primaries;

“negative” implies the addition of that primary to the color sensation being matched by the other two primaries. To avoid the use of negative amounts of color and to provide a standard for calorimetric use, the Commission

Internationale de l’Eclairage (CIE) proposed a set of idealized supersaturated primaries not physically realizable.

and

Ζ(λ) in Figure 5-5 represent the amounts of the idealized primaries required to match any of the pure spectral colors in the visible range indicated on the abscissa. These particular curves curve for the photopic eye (see Figure 5-8) and, thus, provides the luminance primaries are zero; these two primaries provide only chrominance information.

Consider a sample of monochromatic green light of wavelength 520 nanometers. The “tristimulus” values, determined from Figure 5-5, for a particular luminance level might be X = 0.0633, Y = 0.7 100, and Z = 0.0782.

Chroma coordinates are now defined in terms of the tristimulus values by the ratios as follows: so that x + y + z = 1. In the example considered, the chroma coordinates are

X = 0.0633/0.8515 = 0.0743; y = 0.7000/0.8515 = 0.8338; and, z =

0.0782/0.8515 = 0.0918.

If the color to be matched is not integration process must be utilized: monochromatic, a summation or an integration or summation covers the entire visible spectrum. The chroma coordinates are determined by the ratios as previously defined.

Eye Response and Luminous Efficacy 51

400 440 480 520

560 600

640 680

Fig. S-5 International Commission on Illumination (CIE) standard colormixture curves.

Chromaticity Diagram-Each of the three chroma coefficients defines the relative proportion of the three CIE primaries required to match the color of the sample. Because the sum of the three chroma coefficients is unity, it is only necessary to specify two of them, x and y; the third, z, may then be obtained by subtracting x and y from 1. The color may then be specified by a point on a two-dimensional graph as given in Figure 5-6, where x and y each run from 0 to 1.

Each point on the chromaticity diagram specifies chromaticity (hue and saturation) independent of luminance. The locus of all spectral colors

(identified in nanometers) is plotted on this diagram. The open end of the spectral locus is closed by a nonspectral magenta. The standard CIE primaries are represented by the points x = 0, y = 1; x = 0, y = 0; and, x = 1, y = 0. The locus of black bodies at various temperatures (in degree K) is shown by the

52

0.7

Electro-Optics Handbook

/ S P E C T R U M LOCUS

BLACKBODY LOCUS

Fig. 5-6 CIE chromaticity diagram of spectral colors closed by non-spectral colors.

arched curve in the center of the diagram. Those points located in the central region of the diagram, including the segment of the blackbody locus between

2500 K and 12,000 K, are recognized as “white” depending upon the particular adaptation conditions of the observer.

Although color matching was originally done by human observers, calorimetry today is generally done indirectly. Spectroradiometric data are obtained for the sample to be matched and specifications are computed using the tristimulus curves of Figure 5-5 and the chromaticity diagram of Figure

5-6. Classification of ordinary colors by this technique provides matching that provides close correspondence for over 90% of the population.

Eye Response and Luminous Efficacy 53

5.4 SPECTRAL LUMINOUS EFFICACY AND SPECTRAL LUMINOUS

EFFICIENCY

Spectral Luminous Efficacy (Photopic Vision)-Spectral luminous efficacy

(formerly luminosity factor) of radiant flux

Κ(λ) is the quotient of the luminous flux at a given wavelength by the radiant flux at that wavelength.

Hence,

(5-1)

The maximum value of the K(X) function occurs at a wavelength of about

555 nm and has a value of 673 lm W

-1

Spectral Luminous Efficiency (Photopic Vision)-Spectral luminous effi-

wavelength to the value of the luminous efficacy (673 lm W

-1

) at the wavelength of maximum luminous efficacy. Accordingly,

V(h) =

Κ(λ)/673

(5-2)

Spectral Luminous Efficacy and Spectral Luminous Efficiency (Scotopic

Vision)-The corresponding quantities for scotopic vision are spectral the expression

V’(h) =

Κ (λ)/1725

(5-3)

The value 1725 lm W

-1

is the maximum of the spectral luminous efficacy function for scotopic vision and occurs at a wavelength of about 510 nm.

Tabulated values for

ς(λ) and

ς (λ) are given in Figure 5-7. Graphical and

Κ (λ) are shown in Figures 5-8 and

5-9.

It should be noted that all photometric measurements are based on the spectral luminous efficacy and spectral luminous efficiency for photopic vision.

The difference in peak values between luminous efficacy for photopic vision and scotopic vision is not attributable to their responsivity differences but is due to the fact that the standard candela radiates less energy in the blue-green region (where scotopic vision peaks) than in the yellow-green region (where photopic vision peaks). Moreover, scotopic vision covers a narrower region of the spectrum than photopic vision.

54

Wavelength nm

570

580

590

600

610

620

630

640

650

660

670

680

690

700

710

380

390

400

410

420

430

440

450

460

470

480

490

500

510

520

530

540

550

560

0.8620

0.9540

0.9950

0.9950

0.9520

0.8700

0.7570

0.6310

0.5030

0.3810

0.2650

0.1750

0.1070

0.0610

0.0320

0.0170

0.0082

0.0041

0.0021

0.00004

0.00012

0.0004

0.0012

0.0040

0.0116

0.0230

0.0380

0.0600

0.0910

0.1390

0.2080

0.3230

0.5030

0.7100

Electro-Optics Handbook

0.00059

0.00221

0.00929

0.03484

0.0966

0.1998

0.3281

0.4550

0.5672

0.6756

0.7930

0.9043

0.9817

0.9966

0.9352

0.8110

0.6497

0.4808

0.3288

0.2076

0.1212

0.0655

0.03325

0.01593

0.00737

0.003335

0.001497

0.000677

0.0003129

0.0001480

0.0000716

0.00003533

0.00001780

0.00000914

Fig. 5-7 Relative spectral luminous efficiency values (from Table II, Chapter

1 of Kingslake, Reference 11 and Table 6j-1, page 6-l 40 of American Institute of Physics Handbook, Reference 6, with permission) (Part 1 of 2)

Eye Response and Luminous Efficacy 55

.

Wavelength nm

720

730

740

750

760

770

780

0.00105

0.00052

0.00025

0.00012

0.00006

0.00000

. . . . . .

0.00000478

0.000002546

0.000001379

0.000000760

0.000000425

0.000000241

0.000000139

Fig. 5-7 Relative spectral luminous efficiency values (from Table II, Chapter

1 of Kingslake, Reference 11 and Table 6j-1, page 6-140 of American Institute of Physics Handbook, Reference 6, with permission) (Part 2 of 2)

5.5 LUMINOUS EFFICACY AND LUMINOUS EFFICIENCY

In addition to

Κ(λ) and

ς(λ) which relate to a specific wavelength, the which define the overall effectiveness of a given light source in producing luminous flux.

Luminous efficacy K, which may be defined for any radiant source, is the ratio of the total luminous flux to the total radiant flux. Its dimensions are lm W

-1

and it may be used to convert flux in watts to flux in lumens.

constant factor

(5-4) luminous flux from a monochromatic source of the same radiant power at a wavelength of 555 nm.

a function of temperature are shown in Figure 4-4.

5.6 SAMPLE CALCULATIONS INVOLVING LUMINOUS EFFICACY

2045 K. See Figure 4-1. The luminance L v

of this body, using the preceding relations, is calculated as follows:

56

0.5

0.2

Handbook

RED

Fig 5-8 Relative spectral luminous efficiency as a function of wavelength.

The relative response of the human eye to radiation of a given wavelength.

Eye Response and Luminous Efficacy

5 7

E

Fig. 5-9 Absolute spectral luminous efficacy as a function of wavelength. The response of the human eye to radiation of a given wavelength,

58

or,

Electro-Optics Handbook

L v

= 6 0 x 1 0

4 c d m

- 2

2. Assume photopic vision and radiant flux having the following spectral radiant flux.

M v

= the luminous exitance lm m

-2

M e

= the radiant exitance W m

-2

Eye Response and Luminous Efficacy

For a blackbody, the Stefan-Boltzmann law gives

59

Me = 5.67 x 10

-8

(2045)4 = 9.92 x 10

5

W m

-2

If one assumes equal luminance L in all directions, namely 6 x 10

5 nt (cd m

-2

) using the definition given in Section 2.2 for the candela, then (because a blackbody is a Lambertian source),

Therefore,

K=

1.885 x 10

6

9.992 x 10

5

= 1.9 lmW

-1

Note that this result is consistent with the data on Figure 4-4.

References

6. AMERICAN INSTITUTE OF PHYSICS HANDBOOK, Second edition,

McGraw-Hill Book Co., Inc. New York, N.Y., 1962.

10. Wald, G., Brown, P.K., and Smith, P.L., “Iodopsin,” JOURNAL OF

GENERAL PHYSIOLOGY, Vol. 38, No. 5, 623-681, 1955.

11. Kingslake, R., APPLIED OPTICS AND OPTICAL ENGINEERING, Vol.

1 “Light: Its Generation and Modification,” Academic Press, New York,

N.Y., 1965.

12. Graham, C.H., Editor, VISION AND VISUAL PERCEPTION, John Wiley and Sons, Inc., New York, N.Y., 1965.

13. Blackwell, H.R., “Contrast Thresholds of the Human Eye,” J.O.S.A., Vol.

36, No. 11, 624-643, 1946.

14. Middleton, W.E.K., VISION THROUGH THE ATMOSPHERE, University of Toronto Press, Toronto, Canada, 1958.

15. Griffin, D.R., Hubbard, R., and Wald, G. “The Sensitivity of the Human

Eye to Infrared Radiation, ” J.O.S.A., Vol. 37, No. 7, 546, 1947.

Back

61

Section 6

Sources of Radiation

This section concerns radiation from the most important natural sources (sun, moon, stars and sky) and from lamps. Lasers and light-emitting diode sources are discussed in Section 9.

6.1 THE SUN

The sun’s irradiance E just outside the earth’s atmosphere is

= 1390 W m

-2 at mean earth-sun distance

= 1438 W m

-2 at perihelion (3 January 1965)

= 1345 W m

-2 at aphelion (3 July 1965)

See page 16-l of Reference 8.

(6-1) sun at the zenith.

An extensive series of solar-illuminance measurements at the earth’s surface, made by D.R.E. Brown (see page 165 of Reference 16), indicates an

SOLAR IRRADIANCE CURVE OUTSIDE ATMOSPHERE

SOLAR IRRADIANCE CURVE AT SEA LEVEL

CURVE FOR BLACKBODY AT 5900 K

Fig. 6-l Spectral radiance E of the sun at mean earth-sun separation.

Shaded areas indicate absorption at sea level due to the atmospheric constituents shown (Adapted from Reference 8 with permission).

illuminance on a horizontal surface at sea level, with the sun at its zenith in a

“comparatively clear” sky of

E = 1 . 2 4 x 1 0

5 lux (lmm

-2

)

(6-2)

As was noted in equation (6-1), the maximum variation from this average caused by the yearly changes in distance of the earth from the sun is less than

±3.5%. Solar irradiance on the earth’s surface depends on the altitude angle of the sun above the horizon, on the observer’s altitude above sea level, and upon the amount of dust, haze, and clouds in the sky. Figure 6-2 summarizes the results obtained by Brown for various angles of the sun above the horizon. (The altitude angle of the sun at any time and point on the earth’s surface may be calculated by a method given in Appendix C of Reference

16.)

Sources of Radiation

63

True Altitude

Angle of

Center of Sun degrees

40

45

50

55

60

65

70

75

80

85

90

- 1 8

- 1 2

- 6

- 5

- 0.8

0

5

10

15

20

25

30

35

Illuminance

On Horizontal

Surface E lux (or lm m-2)

6.51 x 10

8.31 x 10

3.40

10.8

453

732

4760

1.09 x 10

4

1.86 x 10

4

2.73 x 10

4

3.67 x 10

4

4.70 x 10

4

5.70x 10

4

6.67 x 10

4

7.59 x 10

4

8.50 x 10

4

9.40 x 10

4

10.2 x 10

4

10.8 x 10

4

11.3 x 10

4

11.7 x 10

4

12.0 x 10

4

12.2 x 10

4

12.4 x 10

4

-4

-3

Remarks

Lower limit of astronomical twilight

Lower limit of nautical twilight

Lower limit of civil twilight

Sunrise or sunset

Total change 2.64 magnitudes

(see Section 6.3)

Fig. 6-2 Illuminance levels on the surface of the earth due to the sun

(Reference 16).

6.2 THE MOON

The illuminance E at the earth’s surface caused by sunlight reflected from the moon is affected by the following factors:

1. By the phase of the moon (phase may be expressed by its elongation, i.e., its angular distance from the sun). The relative effect of moon’s phase on the illuminance E is shown in Figure 6-3.

6 4

1.00

0.8

Electro-Optics Handbook

WAXING

WANING

60

120 140

160 180

Fig. 6-3 Relative lunar illuminance as a function of. the moon’s angular

2. By the variation in earth-moon distance during the lunar cycle. There is a total variation of about 26% from this effect.

3. By the differences in reflectance (albedo) of the different portions of the moon surface that are illuminated during the lunar cycle. The moon is about 20% brighter at first quarter (waxing) than at third (waning) due to differences in the lunar surface. See Figure 6-3.

Sources of Radiation

6 5

4. By the altitude angle of the moon above the earth’s horizon and by atmospheric effects.

Figure 6-4 gives the computed variation of lunar illuminance E on a horizontal exposed surface at sea level as a function of the moon’s altitude angle. These values assume a comparatively clear sky, mean earth-moon separation, and the mean of the waxing and waning curves in Figure 6-3.

Values are omitted in Figure 64 for cases where the sun is above the horizon.

6.3 THE STARS

The apparent visual magnitude of stars (stellar magnitude) or of other sources is determined by the illuminance that source produces at a point outside the earth’s atmosphere. (See page 107 of Reference 3.) The ratio of the illuminances produced by two sources differing by one magnitude is defined to be

(moonrise)

-0.8° or moonset)

10°

20°

30°

40°

50°

60°

70°

80°

90°

9.74x 10

-4

1.57 x 10

-3

2.34 x 10

-2

5.87 x 10

-2

0.101

0.143

0.183

0.219

0.243

0.258

0.267

2.73 x 10

-4

1.17x 10

-4

4.40 x 10

-4

6.55 x 10

-3

-2

1.64 x 10

2.83 x 10

-2

4.00

x

10

-2

5.12 x 10

-2

6.13 x 10

6.80 x 10

-2

-2

7.22 x 10

-2

7.48 x 10

-2

1.88 x 10

-4

2.81 x 10

-3

7.04 x 10

-3

1.21 x 10

-2

1.72 x 10

-2

2.20 x 10

-2

2.63 x 10

-2

-2

2.92 x 10

3.10 x 10

-2

. . . . . . . . .

3.12 x 10

-5

5.02 x 10

-5

7.49 x 10

-4

1.88 x 10

-3

-3

3.23 x 10

4.58 x 10

-3

5.86 x 10

-3

. . . . . . . . .

. . . . . . . . .

Fig. 6-4 Illuminance levels on the surface of the earth due to the moon

(Reference 16).

6 6 Electro-Optics Handbook

Therefore, two sources having magnitudes m and n, respectively, would produce illuminances having a ratio given by

(6-3) or log

10

E m

- l o g

10

E n

= 0.400 (n-m)

Figure 6-5 contains values of the illuminance E computed in this way from the stellar magnitudes given for a number of sources. The illuminance for a zero magnitude star was taken as the reference for all the calculations to be

2.65 x 10

-6 lm m

-2

.

The spectral distributions of stellar radiation is treated in Reference 3, pages

110 to 115.

The stars provide approximately 2.2 x 10

-4 lux (lm m

-2

) ground illuminance on a clear night. This illuminance is equivalent to about one-quarter of the actual light from the night sky with no moon. The greater portion of the natural light of the night sky, the airglow that originates in the upper source

Candela at 1 meter -13.9

Venus (at brightest) -4.3**

Sirius -1.42+

Zero Mag. Star 0

1st Mag. Star 1

6th Mag. Star 6

1.00

1.39 x 1 0

9.80 x 1 0

2.65 x 10

. 1.05 x 1 0

1.05 x 1 0

-4

-6

-6

-6

-8

*

* Reference illuminance for calculations (page 191 of Reference 17)

** Reference 18, page 27

+ Reference 18, page 74

Fig. 6-5 Illuminance calculated from stellar magnitudes of various sources outside of the earth’s atmosphere. The transmission of the atmosphere for an object observed at the zenith is approximately

79%.

Sources of Radiation

67

atmosphere, is produced by the emission from various atoms and molecules.

Other minor sources of night illuminance are the aurora and zodiacal light caused by the scattering of sunlight from interplanetary particulate matter.

Blackbody radiation characteristics of a number of stars and planets are shown in Figures 6-6 and 6-7. These curves were calculated from temperature and visual magnitude data. The curves peak at the wavelength derived from

Wien’s Displacement Law. See Section

4.2, equation

4-8.

Each curve response) at an approximate value of the visual magnitude of the star.

The spectral irradiance from a typical aggregate of stars is shown in Figure

6-8.

Fig. 6-6 Calculated spectral irradiance from the brightest stars outside of the earth’s atmosphere; m v irradiance (Reference 19).

= visual magnitude at maximum spectral

68 E l e c t r o - O p t i c s H a n d b o o k

1 0

-2

500 1000

Fig. 6-7 Calculated spectral irradiance from planets at the top of the atmosphere; * = calculated irradiance from planets at brightest due only to sun reflectance; GF = inferior planet at greatest elongation;

OPP = superior planet at opposition; QUAD = superior planet at quadrature; # = calculated irradiance from planets due only to self emission; mv = visual magnitude at maximum spectral irradiance

(Reference 19).

6.4 THE SKY

On a clear day, about one-fifth of the total illuminance E at the earth’s surface is from the sky, that is, from sunlight scattered by the earth’s atmosphere. Figure 6-9 lists some approximate levels of scene illuminance from the day and night sky under various conditions.

Figure 6-10 gives approximate values of the luminance L of the sky near the horizon under a variety of conditions. The concept of luminance when applied to the sky may not be readily apparent with respect to the location of the area implied by m2 or the location of the apex of the solid angle implied

Sources of Radiation

69

Fig. 6-8 Probable spectral irradiance from one-square-degree starfield in or near the galactic plane (Reference 20).

by the use of the unit candela. This difficulty may be resolved by considering the method used to measure the luminance of the sky.

Assume a photometer on earth which measures illuminance. Restrict the photometer with a suitable aperture such that a point on its sensitive area can luminance of the sky is L nits (cd m

-2

), the total luminous intensity of the area As is A s

L and the illuminance at the point of observation in a plane solid angle is measured from the point of observation, the distance to the sky

14, p 10.

70 Electro-Optics Handbook

Sky Condition

Approx. Levels of

Illuminance - lux (lm m-2)

Direct sunlight.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . l-l.3 x 10

Full daylight (Not direct sunlight). . . . . . . . . . . . . . . . . . . . . 1-2 x 10

4

5

Overcast day . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

Very dark day. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

3

2

Twilight . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

Deep twilight . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

Fullmoon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

Quartermoon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1 0

-2

-1

-3

Moonless, clear night sky . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

-4

Moonless, overcast night sky . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 10

Fig. 6-9 Natural scene illuminance.

Sky Condition

Approx. Values of Luminance nit (cd m-2)

*The upper surface of a fog or cloud in sunshine may also have this value.

Fig. 6-10 Approximate values of the luminance of the sky near the horizon under various conditions (Adapted from Reference 14 with permission).

On a clear day the color temperature of the sky is approximately 20,000 K to

25,000 K. The intensity of the scattered sky light varies inversely as the fourth power when the size of the particles in the atmosphere causing the

Sources of Radiation

71

scattering is in the order of magnitude of the light wave. Because the short waves, which correspond to the blue and violet colors, are scattered more than the longer waves of red light, the color of the sky is predominately blue.

Figure 6-l1 shows the spectral distribution of the clear sky and that of a blackbody at 25,000 K.

The irradiance from the night sky is due to the following sources (see page

141 of Reference 11):

Zodiacal

Galactic

Scattering from the above

Direct and scattered starlight

Extra-Galactic sources

3 6 0 400 440 480 520 MO 600 640 720

Fig. 6-11 Spectral distribution of sky light on a clear day. Dashed curve shows the spectral distribution of radiation from a blackbody at

25,000 K (Reference 7).

72

Electro-Optics Handbook

An estimate of the average spectral distribution of the night-sky irradiance is plotted in Figure 6-12. This result in photons per second is on a horizontal

Curves giving radiant exitance of blackbodies at 300 K and 400 K have been added for comparison. It is noteworthy that the lower atmosphere emits thermal radiation whose level may be approximated by blackbody radiation at ambient ground temperature. This effect is limited mostly to the far temperatures of objects within the scene are known, then data like that given in Figure 6-12 permit estimation as a function of wavelength of the photons available for low-light-level image formation. Note that Figure 6-12 indicates a greater abundance of photons at infrared than at visible wavelengths.

6.5 SUMMARY OF NATURAL ILLUMINANCE LEVELS

Figures 6-13 and 6-14 provide a summary of the ambient light levels presented in this section. Curves to indicate illuminances under cloudy moonlight may be drawn by displacing downward the given moonlight curves by the same amounts as for cloudy sun curves (compared to the unobscured sun).

More data on spectral distribution of sky and earth background radiance is available in the literature to augment that presented in this section. Examples are the following:

Reference 11, page 141 to 145

Reference 8, chapter 10

6.6 TIME VARIATION OF NATURAL ILLUMINANCE

Figure 6-15 shows the fraction of the time (averaged over a year) that the illuminance on the earth’s surface due to natural light sources exceeds any given value E at three latitudes. It is assumed that the atmosphere is clear.

6.7 LAMP SOURCES

Figure 6-16 lists some of the optical parameters of a variety of continuous light sources. Spectral curves for some of these sources are referenced in the table, and appear in Figures 6-17 to 6-24. Lamps are available in much more variety than can be covered in this table, with various flux levels, spectral characteristics, mechanical dimensions, cooling requirements, etc. Some of these sources can be modulated.

Sources of Radiation

73

I

I I I I I I

I

0 . 4 0 . 5 0 . 6 0 . 7 0 . 8 0 . 9

1 . 0 1.1

1.2

1.3

1 . 4 1.5

Fig. 6 -12 Natural night-sky spectral irradiance on horizontal earth’s surface and the spectral radiant exitance of blackbodies at 300 K and

400

K.

Figure 6-24 gives an example of a fluorescent lamp spectrum of the

“daylight” type. Various spectral distributions are available for these lamps depending on their phosphor and gas filling.

74

Electro-Optics Handbook

10 3

10-l

ALTITUDE ANGLE ABOVE HORIZON

Fig. 6-13 Illuminance levels on the surface

of

the earth due to the sun, the moon, and the sky (Reference 16).

References

3. Wolf, W.L., Editor, HANDBOOK OF MILITARY INFRARED TECH-

NOLOGY, Office of Naval Research, Dept. of the Navy, Washington, D.C.,

1965.

7. Mauro, J.A. Editor, OPTICAL ENGINEERING HANDBOOK, General

Electric Co., Syracuse, N.Y., 1966.

Sources of Radiation

Fig. 6-14 Range of natural illuminance levels (Reference 16).

I L L U M I N A N C E R E Q U I R E D ( E ) - l u x (lm m -2 )

75

ILLUMINANCE R E Q U I R E D ( E ) - f o o t c a n d l e s (Im ft

-2

)

Fig. 6-15 Fraction of time natural illuminance exceeds a specified level E.

8. Valley, S.L., HANDBOOK OF GEOPHYSICS AND SPACE ENVIRON-

MENTS, Air Force Cambridge Research Laboratories, Office of Aerospace

Research, U.S. Air Force, 1965. Also published by McGraw-Hill Book Co.,

New York, N.Y., 1965.

11. Kingslake, R., APPLIED OPTICS AND OPTICAL ENGINEERING, Vol.

1 “Light: Its Generation and Modification,” Academic Press, New York,

N.Y., 1965.

References continued on page 79.

76

Electro-Optics Handbook

Lamp Type

Mercury Short Arc*

(high pressure)

Xenon Short Arc*

Zirconium Arc**

Vortex-Stabilized

4rgon Arc**

DC

Input

Power

200

1.50

loo

A r c

Dimensions

(mm)

Luminous

Flux

2.5 x 1.8

9500

Luminous

Efficacy

47.5

Average

Luminance

Temperature

(K)

(Fig. No.)

250 Fig. 6-17

1.3 x 1.0

12.5 x 6

1.5

(diam.)

3200

250

21

57

2.5

300

3000

(in 3 mm Fig. 6-19 x 6mm)

100

Fig. 6-18

Fig. 6-20

Fluorescent Lamp

Standard Warm White 40

2560 64 -

-

Non-Rotating

Sun

Rotating

* Courtesy, PEK, Inc., Sunnyvale, Calif. ** Adapted from Reference 21 *** Adapted from Reference 22 page 38

Fig 6-16 Typical lamp parameters.

2 0 0 4 0 0 600 800 1000 2000

Fig. 6-17 Spectral distribution of 200 -watt mercury short arc.

Sources of Radiation

400 600 700 800 900

Fig. 6-18 Spectral distribution of 150-watt xenon short arc.

77

200 600 1000 1400 1800 2200 2600

Fig. 6-l9 Spectral distribution of 20-kilowatt xenon short arc.

WAVELENGTH (

A

) - nm

Fig. 6-20 Spectral distribution of 100-watt zirconium concentrated-arc lamp.

RELATIVE SPECTRAL

SPECTRAL RADIANT

Sources of Radiation

79

Fig. 6-24 Spectral distribution of fluorescent daylight lamp.

(References continued from page 75)

14. Middleton, W.E.K., VISION THROUGH THE ATMOSPHERE, University of Toronto Press, Toronto, Canada, 1958.

16. Bond, D.S. and Henderson, F.P., THE CONQUEST OF DARKNESS, AD

346297, Defense Documentation Center, Alexandria, Va., 1963.

17. Allen, C.W., ASTROPHYSICAL QUANTITIES, Second Edition, The

Athelone Press, University of London, London, England.

18. THE OBSERVER’S HANDBOOK 1963, The Royal Astronomical Society of Canada.

19. Ramsey, R.C., “Spectral Irradiance from Stars and Planets, above the

Atmosphere from 0.1 to 100.0 Microns,” APPLIED OPTICS, Vol. 1, No. 4,

July 1962.

20. Soule, H.V., ELECTROOPTICAL PHOTOGRAPHY AT LOW ILLU-

MINATION LEVELS, John Wiley and Sons, Inc., New York, N.Y., 1968.

21. Buckingham, W.D. and Diebert, C.R., “Characteristics and Applications of Concentrated-Arc-Lamps,” J.S.M.P.E., Vol. 47. No. 5, Nov. 1946.

22. PLASMA JET TECHNOLOGY, SP-5033, NASA, Washington, DC., For sale by U.S. Government Printing Office, Oct. 1965.

Back

81

Section 7

Atmospheric Transmittance

If, however, the path is through a gaseous atmosphere, some of the radiation is lost by scattering and some by absorption. Therefore

(7-2)

T a

= the atmospheric transmittance over a designated path

(T a has a value of less than unity)

Atmospheric transmittance T a is a function of many variables: wavelength, path length, pressure, temperature, humidity, and the composition of the atmosphere. The factor Ta defines the decrease in radiant intensity due to absorption and scattering losses along the atmospheric path.

82 Electro-Optics Handbook

7.1 ENTIRE ATMOSPHERE

Figure 7-1 shows the spectral transmittance (in per cent) through the entire atmosphere (from sea level to outer space) along paths inclined to the zenith by angles of 0°, 60°, and 70.5°. These inclinations provide paths within the atmosphere that traverse air masses of ratios 1, 2, and 3, respectively. These curves indicate the net loss from all scattering mechanisms in a fairly clear atmosphere. Besides scattering by air molecules (Rayleigh scattering) there is scattering by the larger aerosol particles (Mie scattering). Rayleigh scattering may be differentiated from Mie scattering by the following relationships; where a is the radius of the scattering particle and X is the wavelength of the radiation. See Reference 24.

Various regions of absorption are indicated on Figure 7-1. The most important are due to water vapor (H20), carbon dioxide (C02), and ozone

( O

3

). For most applications, the absorption by the other constituents is negligible.

7.2 HORIZONTAL-PATH TRANSMITTANCE

Figure 7-2 shows the atmospheric spectral transmittance over a 1000-foot absorption effects are shown on this figure.

The transmittance of the atmosphere Ta over a path length R for radiation of wavelength X may be expressed by

(7-3)

Equation 7-3 is valid only for very narrow wavelength bands, such as laser transmissions, and for transmission on a horizontal path through an atmosphere of uniform composition.

Sometimes the attenuation coefficient for each of several atmospheric constituents can be calculated separately and summed to obtain the total effect of transmittance. Figure 7-3 shows the sea level attenuation coefficient for a horizontal path in a model clear standard atmosphere (sea-level visibility approximately 23.5 kilometers). This coefficient is the sum of the ozone absorption coefficient, the Rayleigh scattering coefficient, and the aerosol scattering coefficient.

Atmospheric Transmittance 83

I

Fig 7-l Spectral transmittance of the earth's atmosphere for varying optical air masses (Adapted from Reference 23 pp 25 and 26 with permission).

ozone

(7-4)

The effects of ozone absorption are most pronounced in the ultraviolet region of the spectrum and become negligible at longer radiation wavelengths. The

84

100

80

6 0

40

20

0

0 . 5

100

80

60

40

20

0

4 . 0

Electro-Optics Handbook

1 .0

1 . 5 2 . 0 2 . 5

3 . 0 3 . 5

4 . 0

I

8 . 0

-

8 . 5 9 . 0 9 . 5

I I

I I I I

10.0

11.0

12.0

13.0

14.0

15 16 1 7 18 19 20 21 22 23 24 25

Fig. 7-2 Transmittance of 1000-ft horizontal air path at sea level containing

5.7-mm precipitable water at 79° F (From Reference 2.5 with permission).

is a complex function of particle size, shape, refractive index, scattering angle, and wavelength.

Absorbers other than O

3

, such as water vapor and carbon dioxide, are not included in the model of Figure 7-3. The absorption effects, which are highly dependent upon wavelength and absorber concentrations, may be determined by methods such as the one given in Section 10.2 of Reference 8. These effects, however, are generally negligible for narrow band radiation at the specific wavelengths plotted in Figure 7-3.

Atmospheric Transmittance

0.:

85

0.03

0.02

I I I I I I I I

0.2 0.3 0.4 0.5 0.7 1 2 3 4

Fig. 7-3 Calculated atmospheric attenuation coefficients for horizontal transmission at sea level in a model clear standard atmosphere.

Points are plotted from data in Table 7-4 of Reference 8. Absorption by H

2

0 and CO

2

, not included, may be appreciable at wavelengths other than those at plotted points.

86

Electro-Optics Handbook

Figure 7-4 shows how each of the three horizontal attenuations of equation taken from Reference 26 are included in Figure 7-4 for comparison.

0.6

0.4

0.2

0 2 4 6

ALTITUDE - km

8 10

0

2 4

6

ALTITUDE - km

8 10

Fig. 7-4 Atmospheric attenuation coefficients for horizontal transmission of

Curves are plotted from model clear standard atmosphere data in

Table 7-4 of Reference 8.

Atmospheric Transmittance

87

Scattering by water droplets (rain, fog, and snow) is treated by Gilbertson on pages 87 through 91 of Reference 27. According to Gilbertson, the scattering coefficient in rainfall is independent of wavelength in the visible to far infrared region of the spectrum and may be estimated by the equation r =

7.3 HORIZONTAL VISIBILITY

“Visibility range”, “visibility”, and “meterological range” are all names given

R. Middleton (Reference 14, pps 68, 103 through 105) shows that the

(7-6) different kinds of weather.

7.4 CALCULATION OF ATMOSPHERIC TRANSMITTANCE IN THE

This section gives a simplified method for calculating the transmittance of the atmosphere over various path lengths at various altitudes for both horizontal and slant paths. Following this simple method are some calculated results for a standard model of a clear atmosphere.

The simplified calculation procedure uses Figures 7-6 and 7-7. Figure 7-6 the condition of the atmosphere - the latter being identified either by the visibility range or by a general descriptive phrase on the figure. It will be noted that Figure 7-6 follows directly from the “total sea level” curve in

Electro-Optics Handbook

Fig. 7-5 Atmospheric attenuation coefficient for visible light-extinction coefficient-as a function of daylight visibility range-sometimes called "visibility ” or “"meteorological range. ”

Figure 7-3 (which applies to the standard clear atmosphere with a visibility of

(23.5) which may be obtained from Figure 7-5. The line structure of atmospheric absorption due to water vapor, carbon dioxide, and other absorbers such as those shown in Figure 7-2 is therefore not accounted for in the simplified method.

either of two cases. The lower curve gives the correction factor for horizontal paths at specified altitudes, and the upper curve gives the correction factor

Atmospheric Transmittance

89

Fig. 7-6 Approximate variation of attenuation coefficient with wavelength at sea level for various atmospheric conditions. Neglects absorption by water vapor and carbon dioxide.

Electro-Optics Handbook

F O R SLANT P A T H S F R O M

AT ALTITUDE h

0 2

I

8 1O

I I

12 14

ALTITUDE (h) - THOUSANDS OF FEET

I

I

3 4

A L T I T U D E (h) - k m

I I I I I I

16 18 20

5

I

6

I

22

Fig. 7-7 Approximate ratio of attenuation coefficient to sea-level value for slant paths and horizontal paths. Neglects absorption by water vapor and carbon dioxide.

for slant paths from sea level to a specified altitude. The horizontal-path curve is taken from the standard clear atmosphere model of Table 7-4 in

Reference 8 assuming that non-clear atmospheres have similar profiles. The slant-path curve is obtained by integrating an exponential approximation of the standard atmosphere over the appropriate paths and is presumably less accurate than the horizontal-path curve.

A better calculation for slant-path transmittance through the atmosphere can be obtained by using the data of Table 7-4 of Reference 8. Values of the

Atmospheric Transmittance

91

“extinction optical thickness” from the table have been used to calculate the atmospheric transmittance from a point at sea level to points at various altitudes and horizontal ranges from that point. The results are given in

Figures 7-8 through 7-13, each corresponding to a specific radiation wavelength. These figures show contours of constant transmittance. Thus, if the horizontal range and altitude of a given point is known, the transmittance corresponding to the slant path can be estimated directly from the contours.

of the atmosphere (See Figure 7-2) are of particular interest for thermal imaging applications because most terrestrial objects, at temperatures of about 300 K, exhibit a peak in their spectral radiance within that window.

considerably less than in the visible region of the spectrum and the principal attenuation mechanism is molecular absorption, particularly that due to water vapor.

Estimates of atmospheric transmittance on horizontal and slant paths may be made for this window as follows: first the water vapor concentration at sea the precipitable cm of water vapor per kilometer of horizontal-path length) is determined from Figure 7-14 for the particular temperature and relative humidity conditions that apply at sea level. A correction factor, which is a function of altitude h, is then applied to the curves shown on Figure 7-15. These correction factors are based on exponential approximations of water-vapor versus altitude profiles. The corrections are variable as shown in Figure 7-15 between extremes corresponding to empirical height constants, h’, of about 3 km (10,000 feet) and 2 km (6,700 feet). For example, Figure 7-15 indicates that any slant path from 1.8 km (6,000 feet) to sea level should have somewhere between 0.66

and 0.75 of the total water content of an equivalent length horizontal path at even though the curves of Figure 7-16 are based on transmittance data for

Electro-Optics Handbook

3

4

HORIZONTAL RANGE - km

3

7

Fig. 7-8 Contours of constant atmospheric transmittance for radiation at

Curves are plotted from data in Table 7-4 of Reference 8.

shown on Figure 7-16.

Atmospheric Transmittance

93

HORIZONTAL RANGE - km

Fig.

7-9 Contours of constant atmospheric transmittance for radiation at 0.5

are plotted from data in Table 7-4 of Reference 8.

7.6 EFFECTS OF ATMOSPHERE ON IMAGING SENSOR PERFORM-

ANCES

This section summarizes convenient analytical expressions derived by the

Rand Corporation (Reference 28) for predicting the effects of atmospheric scattering and absorption on the performance of several optical sensors including the human eye, photographic systems, photoelectric devices, passive infrared sensors, and active gated-viewing systems.

The validity of these equations depends on the relation defined in equation

7-7 for the apparent radiance L’, of an object as observed at a horizontal range R.

L’o = L o

T a

+ L q

( l - T a

)

(7-7) where

L

Ta o

= the inherent zero-range radiance

= the atmospheric transmittance of radiant flux over the path length R

Electro-Optics Handbook

HORIZONTAL RANGE - km

Fig. 7-10 Contours of constant atmospheric transmittance for radiation at

Curves are plotted from data in Table 7-4 of Reference 8.

and L q

= the radiance of the horizon sky measured at an appropriate azimuth

The term L q

( l - T a

) is an expression for the “path radiance” of the atmosphere that intervenes between the source and the sensor. Equation 7-7 is valid for cases of uniform h-radiance of the path and for a spatially homogeneous spectrum of particle sizes and types with negligible absorptions in the spectral band of interest. If the sensor is the human eye, or if sensor performance can be properly determined from photometric quantities, luminance values may be substituted for the radiometric values of L o and L q

.

Not only is the apparent radiance of an object observed through the atmosphere different from its inherent radiance because of atmospheric transmittance and sky radiance effects but the apparent contrast of the object, and similar limits to visual preception, are also modified. The authors of Reference 28 urge the adoption of the term “transferance” function

Atmospheric Transmittance

HORIZONTAL RANGE -km

Curves are plotted from data in Table 7-4 of Reference 8.

(e.g., contrast) observed at some distance through the atmosphere to the same property observed at zero range.

The transferance ratio, in certain cases, is simply equal to the transmittance of the atmosphere. For example, if the limiting noise in an observation is independent of path radiance, as is the case when the path radiance is time object is viewed against the horizon sky, the transferance of the contrast ratio the observation.

However, the transferance of an optical property is in general a complicated function of the atmospheric transmittance and of the radiances of the object developed as follows. Define the ratio of sky radiance to background radiance as

(7-8)

96

Electro-Optics Handbook

HORIZONTAL RANGE - km

Fig. 7-12 Contours of constant atmospheric transmittance for radiation at

Curves are plotted from data in Table 7-4 of Reference 8.

where the radiance or luminance of the horizon sky measured at an appropriate azimuth and the inherent background radiance or luminance

Using equation 7-7, it may be shown that

Atmospheric Transmittance

7

97

2

0

1 2 3 4 5 6 7 8 9

HORIZONTAL RANGE - km

10 11 12 13 14 15

Fig. 7-13 Contours of constant atmospheric transmittance for radiation at

Curves are plotted from data in Table 7-4 of Reference 8.

the background at the horizontal range R.

Figure 7-17 summarizes the expressions for the factors which limit the performance of each sensor type. The effect of the sky/background radiance terrain and a variety of atmospheric conditions is also shown on this figure.

7.7 ATMOSPHERIC BACKSCATTER - ARTIFICIAL ILLUMINATION

This section gives a convenient method for predicting the effects of atmospheric backscatter on image quality when an artificial source near the image sensor is used to illuminate a distant scene. The line-of-sight path through the atmosphere is taken to be horizontal so the atmospheric the separation between illuminator and imaging system is small compared to

98

T E M P E R A T U R E - O F

Electro-Optics Handbook

Fig. 7-14 Water vapor concentration per kilometer path length as a function of temperature and relative humidity.

the range to the nearest illuminated particles in the field of view. Then, the radiance of the atmosphere within the field of view is calculated by summing the backscatter contributions of all illuminated particles on the path between the sensor and the scene. The result is:

(7-9) where,

I

La

G

= radiance of atmospheric backscatter (W m

-2 sr

-1

)

= radiant intensity of illuminator (W sr-l)

= atmospheric attenuation coefficient (m-l)

= backscatter gain of atmospheric particles relative to isotropic scatterers (dimensionless). A suggested value, for

Atmospheric Transmittance

0

0

I

2000

1

I

0 MIDLATITUDE SUMMER

A MIDLATITUDE WINTER

X SUBARCTIC SUMMER

4000

6000 8000

2

I

10000

3

I

12000

I

4

14000

16000

Fig. 7-15 Exponential approximations for the ratios of water vapor concentration p to sea-level values pO for slant paths and horizontal paths. Points shown are for the model atmospheres shown on the figure.

100

Electro-Optics Handbook

R

min

55

Atmospheric Transmittance

101 actor

Ta

Definition and Equivalents

Transmittance of radiant power in the spectral region of interest

= Transferance of signal-to-noise ratio when the limiting noise is independent of path radiance or when path radiance is time separated

= Transferance of contrast of object seen against the horizon sky (Sky/background ratio K = 1)

Application

Passive infrared

Gated viewing systems

Aircraft spotter

Vision at daylight levels

Photographic systems (determines the performance of all contrast-limited sensors)

I

Fig. 7-l 7 Summary of atmospheric transmittance and transferance factors

(Adapted from Reference 28).

where, with the substitution t = x/z,

(7-11)

is one of a family of “Exponential Integrals” (Reference 30). Combine

equations 7-9 and 7-10 to obtain

(7-12)

Equation 7-l 2 may be applied conveniently with the aid of the graph of

E2(z) plotted in Figure 7-20 as a function of z.

102

C L E A R

O V E R C A S T C L E A R

C L E A R

OVERCAST

Electro-Optics Handbook

OVERCAST

SKY/BACKGROUND RADIANCE OR LUMINANCE RATIO (K)

(Adapted from Reference 28).

Atmospheric Transmittance

101 actor

Ta

Definition and Equivalents

Transmittance of radiant power in the spectral region of interest

= Transferance of signal-to-noise ratio when the limiting noise is independent of path radiance or when path radiance is time separated

= Transferance of contrast of object seen against the horizon sky (Sky/background ratio K = 1)

Application

Passive infrared

Gated viewing systems

Aircraft spotter

Vision at daylight levels

Photographic systems (determines the performance of all contrast-limited sensors)

I

Fig. 7-l 7 Summary of atmospheric transmittance and transferance factors

(Adapted from Reference 28).

where, with the substitution t = x/z,

(7-11)

is one of a family of “Exponential Integrals” (Reference 30). Combine

equations 7-9 and 7-10 to obtain

(7-12)

Equation 7-l 2 may be applied conveniently with the aid of the graph of

E2(z) plotted in Figure 7-20 as a function of z.

Atmospheric Transmittance

103

1 2 3 4 7 10

VISIBILITY RANGE (R y

) Y I E L D I N G T R A N S M I T T A N C E ( T a

) OVER A 2-MILE PATH - MILES

20 70

of sky/background radiance or luminance ratio K (Adapted from

Reference 28).

104

Electro-Optics Handbook

Fig. 7-20 Plot of the exponential integral E used.

2

(z) convenient for calculating atmospheric backscatter effects when artificial illuminators are

Example. An example is given of the use of equation 7-12 and Figure 7-20 in predicting some effects of atmospheric backscatter on image quality. Assume the following parameters apply:

= illuminator wavelength = 850 nm

= 0.126 km

-1

(horizontal, path at sea level through standard clear atmosphere; see Figure 7-6)

= target reflectance = 0.4

G

= scene background reflectance = 0.6

= 0.24

R

min

= 14.3 m

R

max

= 1 0 0 0 m

Atmospheric Transmittance 105

First, the radiance La due to the atmosphere backscatter alone is evaluated.

is kept separate because in the final computation of contrast it will divide out. Use of equation 7-12 and Figure 7-20 gives

(.00757) [70(.98) - .51]

Next, the following comparisons are made:

With

No Atmosphere apparent target radiance

With Atmosphere

[0.515 + (0.4)(0.6)] apparent background radiance

[0.515+(0.4)(0.6)]

106

apparent target-to background

Electro-Optics Handbook

I

0.515 + 0.24

0.515 + 0.36

-1

0.137

One concludes for this example that, at a maximum range or 1000 m, the apparent target-to-background contrast is reduced to 41% of its value at the scene (0.33) by backscatter from the standard clear atmosphere. (Repeating the calculation for a range of 3000 m shows a reduction of apparent contrast to less than 6% of its value at the scene.)

References

8. Valley, S.L., HANDBOOK OF GEOPHYSICS AND SPACE ENVIRON-

MENTS, ‘Air Force Cambridge Research Laboratories, Office of Aerospace

Research, U.S. Air Force, 1965. Also published by McGraw-Hill Book Co.,

New York, N.Y., 1965.

14, Middleton, W.E.K., VISION THROUGH THE ATMOSPHERE, University of Toronto Press, Toronto, Canada, 1958.

23. Carpenter, R.O’B. and Chapman, R.M., EFFECTS OF NIGHT SKY

BACKGROUNDS ON OPTICAL MEASUREMENTS, GCA Technical Report

61-23-A, Geophysics Corporation of America, Bedford; Mass., March 1959.

24. Van de Hulst, H.C., LIGHT SCATTERING BY SMALL PARTICLES,

John Wiley and Sons, Inc., New York, N.Y., 1957.

25. INFRARED COMPONENTS, Brochure No. 67CM, Santa Barbara

Research Center, Goleta, Ca., 1967.

26. Baum, W.A., ATTENUATION OF ULTRAVIOLET LIGHT BY THE

LOWER ATMOSPHERE, PhD Thesis, California Institute of Technology,

Pasadena, Ca., 1950.

Atmospheric Transmittance

4

0

0

Fig. 7-21 Relationship of contrast to the reflectances of target and background.

27. Gilbertson, D.K., STUDY OF TACTICAL ARMY AIRCRAFT LANDING

SYSTEMS (TAALS), Technical Report ECOM-03367-4, AD-477-727,

Defense Documentation Center, Alexandria, Va., Jan. 1966.

28. Bailey, H.H. and Mundie, L.G., THE EFFECTS OF ATMOSPHERIC

SCATTERING AND ABSORPTION ON THE PERFORMANCE OF OPTI-

CAL SENSORS, Memorandum RM-5938-PR, RAND Corporation, Santa

Monica, Ca., March 1969.

29. Deirmendjian, D., “Scattering and Polarization Properties of Water Clouds and Hazes in the Visible and Infrared,” APPLIED OPTICS, Vol. 3, No. 2 Fig.

4, Feb. 1964.

108 Electro-Optics Handbook

30. HANDBOOK OF MATHEMATICAL FUNCTIONS, U.S. Dept. of

Commerce, National Bureau of Standards, Applied Mathematics Series, 55,

1964; fifth printing, Aug. 1966. Contains a discussion of E2(z) and a tabulation of its values.

31. Tatarski, V.I., WAVE PROPAGATION IN A TURBULENT MEDIUM,

McGraw-Hill Book Co., New York, N.Y., 1961.

32. Tatarski. V.I., THE EFFECTS OF THE TURBULENT ATMOSPHERE

ON WAVE PROPAGATION, Translated for NOAA by Israel Program for

Scientific Transaltions, Jerusalem, 1971 Available from U.S. Dept. of

Commerce, NTIS, Springfield, Va.

33. Lawrence, R.S. and Strohbehn, J.W., “A Survey of Clear-Air Propagation

Effects Relevant to Optical Communications,” PROC. IEEE, Vol. 58, Oct.

1970.

34. Kerr, J.R., Titterton, P.J., Kraemer, A.R., and Cooke, CR., “Atmospheric Optical Communication Systems,” PROC. IEEE, Vol. 58, Oct. 1970.

35. Brookner, E. “Atmospheric Propagation and Communication Channel

Model for Laser Wavelengths,” IEEE TRANS. COMM. TECHNOLOGY, Vol.

COM-18, Aug. 1970.

36. Wyngaard, J.C., Izumi, Y., and Collins, S.A., “Behavior of the

Refractive-Index-Structure Parameter near the Ground,” J. OPT. SOC. AM.,

Vol. 60, Dec. 1971.

37. De Wolf, D.A., EFFECTS OF TURBULENCE INSTABILITIES ON

LASER PROPAGATION, RCA Third Quarterly Report TR-72-119 to Rome

Air Development Center, Griffiss AFB, N.Y., Apr. 1972.

Back

109

Section 8

Detection, Resolution, and Recognition

A common problem in electro-optics is the detection and resolution of detail in the presence of noise. In Sections 8.1 and 8.2, two approaches are considered for detecting pulses in the presence of noise. The first analyzes detection of signal pulses in white noise. The second considers detection of signal pulses in quantum noise. The first approach is applicable when large numbers of photons are available and the fluctuations in the signal are small compared to the additive noise. The second approach is used when the signal and the noise are both characterized by low photo-electron generation rates.

Section 8.3 relates image resolution to modulation transfer function (MTF) and to equivalent rectangular passband (Ne). Section 8.4 considers some aspects of visual interpretation of displays. In Section 8.5 the Rand

Corporation’s model for target detection/recognition is given.

8.1 PULSE DETECTION IN WHITE NOISE

The problem treated in this section is that of detecting a rectangular signal threshold detector is used. The actual pulse shape is not critical. The signal plus noise is passed through a matched filter (or correlator) having a of the matched filter on the rectangular signal pulse and on the white noise.

At the filter output, the signal current component is denoted i s

, a triangular pulse of peak amplitude I s

(the same amplitude as the rectangular input

110

Electro-Optics Handbook

(8-1)

-

ALARM

where,

Fig. 8-1 Schematic representation of threshold detection process.

W =

= noise bandwidth of matched filter (Hz)

7 = input pulse duration(s)

(8-2) the output noise current i n exceeds the threshold value I t

of the detector.

This rate is given by Rice (equations 3.3-12 and 3.3-14 of Reference 40) as

(8-3) which decreases rapidly as the threshold value I t

is raised.

the instant of signal peak, i.e.,

(8-7)

If the

threshold I t has been set according to equation 8-3 to achieve a given false alarm rate, then the peak-signal-to-rms-noise-current ratio I s

/I n required to obtain a specified probability of detection Pd may be found from equation

8-7. The relations are shown graphically in Figure 8-2. Equation 8-7 is plotted in Figure 8-3 as a function of I s

/I n for selected values of the parameters

NOISE ALONE

111

(8-4)

( 8 - 5 )

(8-6)

CURRENT -

Fig. 8-2 Graphical relations between probability of detection P d probability

Electro-Optics Handbook

1

I

Fig. 8-3 Probability of detecting a rectangular pulse in white noise.

maximum range R mx of 10 km. If a matched filter and threshold detection are used, what signal-to-noise ratio and what threshold-to-noise ratio are required to obtain a probability of detection of 99.9% and a false detection no more than one time per thousand pulses?

In order to range to 10 km, the rangefinder must be gated open for a total interval of where c is the velocity of light. The average false alarm rate FAR is thus

Detection, Resolution, and Recognition

F A R =

1

1000 x 67 x 10

-6

= 15 s

-1

Hence,

113

= 1.5 x 10

-6

8-3 yields a peak-signal-to-rms-current ratio (I s

/I n

) of 8.1.

The required threshold-to-noise setting It/In is obtained from equation 8-3 and may be solved as follows:

Note this latter ratio could also have been read directly from Figure 8-3 by realizing that Pd = 50% where I s

/I n

= It/In.

Note that the rms noise current I n

, dependent upon white noise power spectral density W and the filter noise bandwidth B, is found using equation

8-1.

8.2 PULSE DETECTION IN QUANTUM NOISE

When the signal and noise are small, the arrival of photons in a given small time interval is a small number and independent of the arrival of photons in any other small time interval. This condition is often the case, for example, when a photomultiplier detector is used in a laser range finder and there is low background noise. In such cases one may assume a Poisson distribution for evaluating the probability that in a certain time interval the number n of photons arriving or the number of photoelectrons generated or events occuring will be exactly equal to r; namely

P(n = r) = e

-n

( n ) r r!

(8-8)

114

Electro-Optics Handbook

number n of such events in that interval is counted, then a threshold number n t

can be established as a criterion for deciding whether a signal pulse is present or not. It follows from equation 8-8 that the probability of at least n t events is

(8-9)

Equation 8-9 is plotted in Figures 8-4 and 8-5 in two parts (from data in

Reference 41); Part I, shown in Figure 8-4, estimates the probability of counts n of signal plus noise events ranging between 0.2<n<35 per time interval. Part 2, shown in Figure 8-5, estimates the probability of false alarm

Example. When no signal is present, an average of two events occurs per observation interval while sixteen occur on the average when a signal is present. If a false alarm rate of about one per ten thousand observations or less is allowable, where should the threshold be set and what is the detection probability?

From Figure 8-5, a threshold n t

of 9.5 events or higher will meet the false alarm rate specification. Setting n t

to 10 (next higher integer) and consulting

Figure 8-4 shows that the detection probability is 0.955.

8.3 MTF (MODULATION TRANSFER FUNCTION) AND CTF (CON-

TRAST TRANSFER FUNCTION)

The MTF is a measure of the resolution of an imaging system sufficiently general to apply not only to the optics, but also to image intensifiers, camera tubes, video amplifiers and displays as well. The MTF is the sine-wave spatial-frequency amplitude response. It equals unity for sufficiently low spatial frequencies. Spatial frequency (N) refers to the number of cycles per unit length. The main usefulness of the MTF is that it permits cascading the effects of the several major components of a system in determining a measure of resolution of the overall system. The MTF of the overall system at a given spatial frequency is the product of the MTF’s of the elements.

The CTF is the square-wave spatial-frequency amplitude response. Unlike

MTF’s, CTF’s cannot be cascaded to evaluate overall system response.

Amplitude response in this form, however, is frequently quoted because it is easier to measure. Either form of response can be converted to the other as shown in equations 8-10 and 8-11,

Detection, Resolution, and Recognition

0.9999

.9995

.999

.998

115

THRESHOLD NUMBER n t

Fig. 8-4 Probability of nt or more random events with Poisson distribution the threshold number nt (Part 1 of 2).

116

Electro-Optics Handbook

THRESHOLD NUMBER nt

Fig. 8-5 Probability of nt or more random events with Poisson distribution

(Part 2 of 2).

Detection, Resolution, and Recognition 117

The term involving C (9N) is omitted in equation 8-10 because it is zero.

(8-11)

Figure 8-6 presents a useful set of computations for a system with a

Gaussian-shaped MTF. The MTF is normalized so that the response is 1% at a spatial frequency of 100. N e is the equivalent rectangular passband

(Reference 42) according to the formula definition given in Figure 8-6. The usefulness of the N e measure is its ability to express the overall response by one number. A further advantage is that the subjective appearance of imagery from systems with equal N e but differing limiting resolution tends to be very similar. N,’ is the equivalent rectangular passband for spatial frequencies from

0 to N as shown in Figure 8-6.

Degradation of MTF by Various Forms of Image Motion. Angular Angular

stabilization errors can produce smear and degrade camera resolution. The effects of four types of high-frequency (e.g. vibration) errors can be calculated from equation 8-12.

(8-12) where, average intensity level at location X t p

= exposure time

N = spatial frequency f(t) = a type of image-motion disturbance (periodic triangular, periodic sine wave, periodic square wave, Gaussian random displacement).

118

Electro-Optics Handbook

Normalized Normalized Normalized

Spatial MTF CTF

Frequency Sine-Wave * Square-Wave

(N)

See Note

Response Response

M(N) C(N)

0 100

2 99.8

5

98.9

10

95.5

20 83.2

29.2 67.5

30 66.1

40 47.9

50

31.5

60 19.1

70

10.5

80

80.7

87.2

3.0

92.2 2.0

100 1.0

MTF = exp (-4.605 x 10

-4

N2)

100

100

100

100

98.0

84.8

83.2

61.0

40.2

24.3

13.4

6.6

6.4

3.8

2.5

1.3

N’e

Equivalent

Rectangular

Pass Band

To Spatial

Frequency N

0

2.0

5.0

9.7

17.8

23.1

23.4

26.7

28.3

28.9

29.1

29.2

29.2

29.2

29.2

29.2

NOTE: Normalized spatial frequency (N) is usually expressed in units of cycles/unit length for MTF and in units of line-pairs/unit length for CTF.

1.03

1.37

1.71

2.05

2.40

2.74

2.76

2.99

3.16

3.42

0

0.0685

0.171

0.342

1

Fig. 8-6 Various parameters related to a Gaussian-shaped MTF (Modulation

Transfer Function).

Equation 8-12 can be solved for periodic triangular, sine or square-wave disturbances by making the exposure time, t p

, equal to one or more periods of the disturbance. The amplitude of I x

is shown in Figure 8-7 for several types of disturbances. A summary of the effects of these high-frequency errors is also provided in the table of Figure 8-8. The Gaussian random displacement-type disturbance can also be solved by appropriate analysis and the results are included in Figure 8-8.

Detection, Resolution, and Recognition

0.3

0.4

0.5

0.6

0.7

Fig. 8-7 MTF for several high-frequency image motions.

8.4 DISPLAY INTERPRETATION

Limiting Resolution. It is common practice to specify the resolving capability

of an electro-optical imaging system in terms of the image of a black and white bar chart such as the RETMA television test pattern. The line limit represents the spatial frequency at which the observer’s eye can no longer discriminate differences in the light and dark transitions in the bar image. It is assumed that the frequency response of the system is poorer than that of the eye, so that the line limit is truly a measure of the system’s capability, and not that of the eye. (Reference 43).

Because the eye is normally considered to require an image contrast about three percent in order to appreciate the light-to-dark transitions in the bars, the limiting resolution in line-pairs/mm or in line-pairs per picture width can be considered as the spatial frequency at which the MTF (modulation transfer function) has fallen to a value of three percent. The limiting resolution measure of an electro-optical imaging system is therefore related to one point on the MTF. Contrast is here defined as the ratio of the imaged difference in luminance between the dark bar and its background to the luminance of the background. See Section 11.

120

Electro-Optics Handbook

Type of Image

Motion

Error

Waveform

rms

Amplitude

Triangular

Waveform

Sine-Wave

Response

(MTF) in line pairs/ unit length

Sine Waveform

Square

Waveform

Gaussian

Random

Displacement

A integral is taken only to the first zero of the MTF for sine waveforms and square waveforms because the integrals do not converge for these two cases as the upper limit approaches.

**Zero-order Bessel function of first kind.

Fig. 8-8 Summary of the effects of high-frequency stabilization errors.

Line Resolution Requirements. Figure 8-9 summarizes conclusions from one

set of measurements on the capability of humans to perceive single military targets (standing man to tank size) as a function of the limiting resolution per target minimum dimension (Reference 44).

Angular Threshold of Eye. The probability of seeing an object is influenced

not only by the field luminance, the contrast of the object with respect to the scene background and the complexity of the scene, but also by the angular

Detection, Resolution, and Recognition 121

Task

Line Resolution per Target

Minimum Dimension

Detection 1.0 ± 0.25 line pairs

Orientation 1.4 ± 0.35 line pairs

Recognition 4.0 ± 0.8 line pairs

Identification 6.4 ± 1.5 line pairs

Fig. 8-9 Line resolution requirements.

subtense of that object at the eye of the observer. Under ideal conditions the eye can resolve about 30 seconds of arc. In most practical situations, however, the angular threshold of the eye is much larger than that. For example, it has been shown (Reference 45) that a target appearing in a complex field of confusion elements must subtend about 12 minutes of arc to enable a high (97 percent) probability of recognition. With a high resolution complex image, for which line resolution does not enter as a limiting and confounding factor, it appears that 6 to 12 minutes of arc are required for the typical visual acquisition and recognition tasks.

Visual Search Time. The time required to search a particular frame may be

computed analytically from knowledge of the eye’s fixation time and the angular size of the display, an approach discussed by Simon (Reference 46).

Two assumptions are made:

(1) a single fixation requires approximately three-tenths of a second

(2) the circular field of clear vision subtends 5 degrees.

The length of time required to search an entire display field once through is computed by determining the number of nonoverlapping 5° fixations required to cover the field. A display subtending 16° x 16° at the eye would thereby be predicted to require:

16°/5° x 16°/5° x 0.3s = 3.1 s

Imaging sensor performance may be estimated and/or evaluated by application of a target detection/recognition model such as that suggested by the Rand Corporation (Reference 47); namely:

122

Electro-Optics Handbook

(8-13) where P r

is the probability that a target will be recognized on the display; Pr is the probability that the observer, searching an area that is known to contain a target, looks with his foveal vision for a specified glimpse time (l/3 s) in the direction of the target; P

2

is the probability that if the displayed target image is viewed foveally for one glimpse period it will, in the absence of noise, have sufficient contrast and size to be detected; P

3

is the probability that if a target is detected, there will be enough detail shown for it to be an overall degradation factor arising from noise.

The probability P

1

is difficult to estimate because it is affected (1) by the solid angle presented to the eye of the search field, (2) by the time available to search it, (3) by the number of confusing elements within the scene, and

(4) by the availability of any “cues” or a priori information as to where to look on the display. The model employs the relation

(8-14) where, a t

= area of target

A, = area to be searched

= time

= congestion factor, usually between 1 and 10, for most real imagery of interest.

The probability of detection, P

2

, at the threshold contrast C t

, is by definition

50%. A useful approximation for P2 at other contrasts C available at the eye is given by

The other two factors in equation 8-13 are also plotted in Figure 8-10, being calculated respectively from

Detection, Resolution, and Recognition

and

123

where,

(8-18) is the number of resolution cells contained in the minimum projected target

CC

is angular resolution of the sensor, R is the target range, and SNR is the displayed signal-to-noise ratio. (A more complete treatment of the effect of noise in electro-optical displays is recent work reported in

Reference 48).

0.8

Fig. 8-l 0 Probability factors used in the Rand Corporation model (Reference

47) for target detection and recognition

124

Electro-Optics Handbook

Note that an expression for the probability of detection alone (without recognition) is obtained by considering only three of the factors in equation

8-13; namely

References

38. North, D.O., “An Analysis of the Factors which Determine Signal/Noise

Discrimination in Pulsed-Carrier Systems,” PROC IEEE, Vol. 5 1, July 1963.

39. Schwartz, M., INFORMATION TRANSMISSION, MODULATION, AND

NOISE, McGraw-Hill Book Co., New York, N.Y., 1959.

40. Rice, S.O., “Mathematical Analysis of Random Noise,” THE BELL

SYSTEM TECHNICAL JOURNAL, Vol. 23, No. 3, July 1944 and Vol. 24,

No. 1, Jan. 1945.

41. POISSON DISTRIBUTION, General Electric Co., Defense Systems

Department, D. Van Nostrand Co., New York, N.Y., 1962.

42. Schade Sr., O.H., “A New System of Measuring and Specifying Image

Definition,” NATIONAL BUREAU OF STANDARDS CIRCULAR 526,

231-258, 1954.

43. SPECIFICATION FOR EIA(RETMA) RESOLUTION CHART 1956,

Industrial Electronics Bulletin No. 2, Electronic Industries Association,

Engineering Department, New York, N.Y., 1956.

44. Johnson, J., “Analytical Description of Night Vision Devices,”

PROCEEDINGS OF THE SEMINAR ON DIRECT-VIEWING ELECTRO-

OPTICAL AIDS TO NIGHT VISION, Biberman, L., Editor, Institute for

Defense Analyses Study S254, Oct. 1966.

45. Steedman, W., and Backer, C., “Target Size and Visual Recognition,”

HUMAN FACTORS, Vol. 2, Aug. 1960.

46. Simon, C., “Rapid Acquisition of Radar Targets from Moving and Static

Displays,” HUMAN FACTORS, Vol. 7, June 1965.

47. Bailey, H.H., “Target Detection Through Visual Recognition: A

Quantitative Model,” Rand Corporation, Santa Monica, Ca., Feb. 1970.

Detection, Resolution, and Recognition

125

48. “Low Light Level Devices: A Designer’s Manual,” Report R-169, Institute for Defense Analysis, Science and Technology Division, Arlington, Va., Aug.

1971.

49. Coltman, J.W., and Anderson, A.E., “Noise Limitations to Resolving

Power in Electronic Imaging,” PROC. IRE, May 1960.

50. Rose, A., “The Sensitivity Performance of the Human Eye on an

Absolute Scale,” J.O.S.A., Vol. 38, No. 2, Feb. 1948.

Back

127

Section 9

Lasers

Laser action has been observed in various media including crystalline solids, glasses, plastics, liquids, gases, organic dyes, and even jello (Reference 51).

This section contains the current information concerning the characteristics of lasers. The emphasis is on those lasers that have either been proven to be practical or else are the only sources in a particular wavelength range. There are, in addition, indirect sources of coherent radiation such as frequency multiplication and parametric conversion. These indirect sources are discussed in separate parts of this section. For a detailed listing of all known laser transitions and of the nonlinear materials used for up and down conversion, see Reference 52.

The choice of a laser for a particular application involves consideration of the advantages and disadvantages of each type. The development of mode-locking and cavity dumping techniques, of high optical quality, damage-free nonlinear materials, of cw semiconductor lasers, and of the dye lasers has significantly increased the range of options available to the system designer. For high peak power applications the energy storage capacity of insulating solid crystal or glass lasers makes them the optimum choice. Due to their comparatively broad linewidth these lasers as well as the dye lasers are also the optimum lasers offer significant advantages for low power, reliable operation in the visible portion of the spectrum. In particular the He-Cd laser is the optimum choice for the exposure of photoresist materials. In the infrared the CO and

128 Electro-Optics Handbook

applications such as longer wavelengths.

welding or as sources for parametric down conversion to

The reader is reminded that laser radiation may produce injury to the eyes or skin. Appropriate safety procedures for use with lasers of differing power and output wavelengths may be found in the American National Standards

Institute Standard for the Safe Use of Lasers (2136.1).

9.1 CRYSTALLINE LASERS

Figure 9-1 is a list of useful crystalline lasers with their wavelength, mode of operation: pulsed (p) or continuous wave (cw), and typical operating temperature. The emphasis is on lasers that operate at room temperature.

Those dopants listed in parentheses are additional impurities which absorb the pump radiation and transfer the energy to the active ion. Though the multiply doped lasers are not widely used at the present time, several of them are more efficient than the singly doped materials.

It is noticeable from Figure 9-l that there are no lasers listed for wavelengths not compete either in output power or in simplicity of operation with either gas lasers or up conversion of longer-wavelength crystalline lasers. The up-converted or tuned-output crystalline lasers will be discussed in Section

9-4.

As noted in the introduction, mode-locking and cavity dumping are two new particularly adaptable to mode-locking techniques because of its compara-

9.2 GLASS LASERS

9.3 GAS LASERS

Figure 9-2 gives a list of gas lasers which are important at the present time.

The table includes estimates of their output power for different modes of operation. The development of cavity dumping techniques has provided an

Lasers

129

300

300

300

300

300

300

300

300

Operating

Temperature (K)

350

350

300

77

300

300

300

300

230

300

300

300

300

300

300

300

-

Fig. 9-I Crystalline laser systems.

additional output format which is usable with any of the gas lasers. The rapid advances in the area of “chemical” pumping of the molecular lasers and the variety of techniques used make the values given for the output power only a rough guide subject to careful qualification. See Reference 53.

130

Electro-Optics Handbook

0.3454

0.378 1

0.4060

0.42 14-0.4272

0.5419-0.627 1

2.026

3.507

5.575

9.007

0.337 1

0.3324

Typical

15 mW

50 mW

5mW

50 mW

1OmW

Power Output

Maximum

1w

1mW

1 mW

1 mW

1 mW

Mode of

Operation

1

cw cw cw cw cw cw cw cw cw

200 kW

100 mW

P cw

40 mW

200 mW cw cw

1OmW

P, cw

0.5401

1 kW

P

0.5 106

40 kW

P

Ar

(ionized)

0.3511

0.3638

0.4579

0.4658

0.4727

0.4765

0.4880

0.4965

0.5 107

0.5 145

5mW

5mW

0.1 w

0.1 w

50 mW

.3 w

1.0 w

.2 w

.l w

0.35 w

0.35 w

0.75 w

0.3 w

0.4 w

1.5 w

5.ow

1.5 w

.7 w

6.0 W

Fig. 9-2 Some typical gas laser systems. (Part 1 of 2)

cw cw cw cw cw cw cw cw cw cw

Lasers

He-Se

(ionized)

Kr

(ionized)

He-Ne

CN

Transverse

Excitation

Atmospheric

(TEA)

HCN

0.4605-0.6490

(24 lines)

0.5228

0.3507

0.3564

0.4762

0.4825

0.5208

0.5309

0.5682

0.647 1

0.6764

0.7525

0.793 1

0.7993

Typical

Power Output

Maximum

100 mW

20 mW

Mode of

Operation cw cw

150 mW

25 mW

1OmW

cw cw cw

4500 w

1 joule

I

30 mW

I P

200 kW cw

P

1000 w

50 kW

131

Fig. 9-2 Some typical gas laser systems. (Part 2 of 2)

132 Electro-Optics Handbook

9.4 DYE LASERS

The active medium of a dye laser consists of a strongly fluorescing organic compound dissolved in an appropriate solvent. Included in this group are a number of commercial dyes. This medium is pumped with a flash lamp or a laser and is usually operated in the pulsed mode. Continuous operation has recently been obtained by circulating the active medium through the optical cavity and pumping with a cw laser.

The active molecule typically fluoresces over a bandwidth of 35 to 80 nm and lasing action can occur over most of this range. For a particular molecule, wavelength selection is accomplished with cavity mirrors (laser Ah-20 nm), etalon allows one to scan across the fluorescent bandwidth of the active molecule. Use of several different dyes in succession can provide a tuneable output from the available active molecules are unstable and as a result are not practical sources. A number of different materials which can provide a tuneable output are listed in Figure 9-3. Solvents other than those listed may be used. It should be noted, however, that the fluorescent band position is solvent dependent.

Dye

Calcein Blue

1,3 Diphenylisobenzofuran

Fluorscein

Rhodamine 6G

Rhodamine B

Cresyl Violet

Solvent

Ethanol

Ethanol

Aqueous Alkaline

Ethanol

Ethanol

Ethanol

Tuning Range

449 - 4 9 0

484 - 5 1 8

520 - 5 7 0

560 - 6 5 0

590 - 7 0 0

630 - 6 9 0

Fig. 9-3 Some representative dye laser materials.

Lasers

133

Typical output parameters for a pulsed visible dye laser include an energy output of 0.1 joule and peak powers of the order of 2 MW at a rate of 30 p/s.

50 mW can be obtained in a flowing dye system with a spectral bandwidth of less than 0.001 nm.

9.5 SECOND HARMONIC GENERATION AND PARAMETRIC DOWN-

CONVERSION

Second harmonic generation (Reference 56) and parametric up- and down-conversion (References 57 and 58) provide alternative sources of coherent radiation in the ultraviolet to the infrared range. These effects occur be written as field amplitudes. In addition to this symmetry requirement, both energy and momentum must be conserved in the process. For second harmonic generation: and for parametric up- or down-conversion

These equations are the index of refraction matching conditions for the nonlinear processes. Figure 9-4 is a listing of commonly used nonlinear materials.

For second harmonic generation the nonlinear medium is usually placed within the laser cavity in low power applications and outside the cavity when the circulating power can damage it. Examples of frequency doubling are:

Lasers 135

refraction of the nonlinear crystal. The index is changed by applied electric fields, change in the angle of incidence of the pump radiation, or by variation of the temperature of the nonlinear medium.

An example of a parametric oscillator is one pumped by a Q-switched crystal. A lithium niobate crystal is temperature tuned to provide a variable output wavelength in the range from 620 nm to 3500 nm. The output is not continuous in wavelength but occurs in discrete ranges depending upon the particular pump wavelength and the mirrors used. Average output powers of several milliwatts and peak powers of 500 watts can be obtained. In the wavelength range beyond 750 nm, this device offers the only practical source of tuneable coherent radiation.

9.6 P-N JUNCTION LIGHT

SOURCES

In a forward-biased p-n junction, the minority carriers injected across the p-n junction recombine either radiatively, with the emission of photons, or non-radiatively. The photon energy will depend on the nature of the atomic centers involved and the bandgap energy of the crystal. In so-called “direct bandgap” materials such as GaAs, the photon energy is close to the bandgap energy of the material. In “indirect bandgap” materials such as GaP, the luminescence frequently involves impurity levels which shift the photon energy of the emitted radiation to values substantially below the bandgap energy.

Recombination radiation has been observed over a wide range of efficiencies in most of those semiconductors in which p-n junctions can be fabricated.

When the electro-luminescent radiation is incoherent, the diode source is described as a light-emitting diode (LED) type; when the radiation is coherent, the source is described as a laser type.

There are important differences in the nature of the materials needed and the construction of the device for the two types of application. The difference in emission becomes directional, the spectral width decreases to a few tenths of nanometers, and the differential efficiency increases sharply. This change in efficiency is shown in Figure 9-5.

9.6a

P-N JUNCTION LASERS

A practical laser diode has three basic requirements: (1) it must be constructed from a direct bandgap semiconductor; (2) it must have a

136

Electro-Optics Handbook

Fig. 9-5 Typical output curve of GaAs laser diodes.

Fabry-Perot cavity, which consists of two mirror-like surfaces defining the direction of photon flux; and (3) a region must be formed which confines the radiation and the injected carriers. The Fabry-Perot cavity is generally created by cleaving the material along parallel crystal planes either of which may be confinement to a waveguide region is achieved by structuring the dielectric growth of the crystal. Present-day commercial laser diodes are of the heterojunction type (also denoted “close-confinement”) where the refractive index differences in the junction region are obtained by using layers of

(AlGa)As and GaAs. The higher bandgap energy of the (AlGa)As which

Lasers

137

Fig. 9-6 Diagram including some essential features of a p-n junction laser:

adjoins the lasing region of GaAs also provides for carrier confinement thereby resulting in reduced threshold current densities and higher efficiencies than possible in older structures without the heterojunctions.

There are several types of heterojunction lasers with specific advantages peculiar to each. The most widely used commercially available diode

(Reference 59) is the single heterojunction “close-confinement” device

(SH-CC), Figure 9-7b, emitting at approximately 900 nm. It is capable of operating in the pulsed mode at relatively high duty cycle, about 0.l%, with peak power of several watts for single diodes and up to kilowatts for multidiode arrays. By lowering the operating temperature to 77K or less, the close-confined lasers can be operated continuously, provided adequate heat sinking is employed.

More recently, devices have been developed in which the radiation is confined by two (AlGa)As-GaAs heterojunctions (References 60, 61, and 62) as compared to the single heterojunction type, and the width of the mode-guiding region can be adjusted by changing the spacing between the heterojunctions. By reducing the threshold current density to values below continuous wave operation can be obtained at room temperature. Due to the uncertain operating life of room temperature cw lasers, such devices are not yet commercially available.

The large optical cavity (LOC) laser diode, shown in cross section in Figure

9-7d, allows the construction of devices having rather wide well-controlled

138

TYPE

Electro-Optics Handbook

JUNCTION TYPE.

CAVITY (LOC)

TYPE.

Fig. 9- 7 Illustrations of various laser cross sections showing optical intensity

I, variation of bandgap Eg, and index of refraction n.

mode-guiding regions. This diode can operate with higher efficiencies and at higher temperatures than possible with the single heterojunction type.

Developmental devices of this type are capable of operation at a duty cycle of about 1 percent.

As lasers can be varied by varying the composition of the devices. Figure 9-8 indicates how the threshold current

Many other III-V, II-VI, and lead salt compounds have been operated as lasers

(Reference 52) at wavelengths ranging from the near ultraviolet to the midand are not commercially available.

139

Fig. 9-8 Nominal dependence of threshold current density in single heterojunction close-confinement (SH-CC) and double heterojunction

9.6b LIGHT-EMITTING DIODES (LED’s)

Incoherent or spontaneous emission devices (Reference 63) are available covering a broader range of the spectrum than laser diodes cover. Higher brightness sources in the visible portion of the spectrum (Reference 64) have green), and GaN (blue, green and, yellow). See References 65,66,67, and 68.

GaN has also produced near ultraviolet dc electroluminescence at room production and are commercially important as display devices.

140 Electro-Optics Handbook

Figure 9-9 lists many of the materials in which electroluminescence has been observed. The range shown for GaP is due to the incorporation of different impurities in the material which produces a range of colors from red to yellow (red plus green) to green.

Figure 9-10 indicates which of these materials has shown laser and light-emitting action and Figure 9-11 is a compilation of some of the important engineering parameters associated with the electroluminescent diodes commercially available.

References

51. Hansch, T.W., Pernier, M., Schawlow, A.L., “Laser Action of Dyes in

Gelatin,” J. QUANT. ELEC. Vol. QE-7, No. 1, Jan. 1971.

52. Pressley, R.J., Editor, HANDBOOK OF LASERS, Chemical Rubber Co.,

1971.

53. Jeffers, W.Q., Editor, “Third Conference on Chemical and Molecular

Lasers,” J. QUANT. ELEC., Vol. QE-9, No. 1, Jan. 1973.

54. Furumato, H.W. and Ceccon, H.L., “Ultraviolet Organic Liquid Lasers,”

J. QUANT. ELEC. Vol. QE-6, No. 5, May 1970.

55 Warden, J.T. and Gough, L., “Flashlamp-Pumped Laser Dyes: A Literature

Survey,” APPL. PHYS. LETT., Vol. 19, No. 9, Nov. 1971.

56. Kleinman, D.A., “Theory of Second Harmonic Generation of Light,”

PHYS. REV., Vol. 128, No. 4, Nov. 1962.

57. Oshman, M.K., and Harris, S.E., “Theory of Optical Parametric

Oscillation Internal to the Laser Cavity,” J. QUANT. ELEC., Vol. QE-4, No.

8, Aug. 1968.

58. Harris. SE., “Tunable Optical Parametric Oscillators,” PROC. IEEE, Vol.

57, No. 12, Dec. 1969.

59. Kressel, H. and Nelson, H., “Close-Confinement Gallium Arsenide PN

Junction Lasers with Reduced Optical Loss at Room Temperature,” RCA

REVIEW, Vol. 30, No. 1, March 1969.

142

Electro-Optics Handbook

PbSe

PbTe

InSb

PbS

InAs

Crystal

I

I

Wavelength

INJECTION LASER SOURCES

8.5

6.5

5.2

4.3

3.15

GaSb

1.6

0.91

SiC

LED SOURCES

I

0.855

0.64

0.627

0.62

0.565

0.68

0.456

Fig. 9-10 Partial listing of injection laser and LED sources.

References continued from page 140

60. Hayashi, I., Panish, M.B., Foy, P.N., Sumski, S., “Junction Lasers which

Operate Continuously at Room Temperature,” APPL. PHYS. LETT., Vol. 17,

No. 3, Aug. 1970.

61. Kressel, H., Lockwood, H-F., Hawrylo, F.Z., “Low-Threshold LOC GaAs .

Injection Lasers,” APPL. PHYS. LETT., Vol. 18, No. 2, Jan. 1971.

62. Kressel, H., Lockwood, H.F., Ettenberg, M., “Progress in Laser Diodes,”

IEEE SPECTRUM, Vol. 10, No. 5, May 1973. (A review of all laser types).

References continued on page 144

Crystal

300

I

300

I

300

Laser

I 77

I

300

I

300

I

144 Electro-Optics Handbook

63. Bergh, A.A. and Dean, P.J., “Light-Emitting Diodes,” PROC. IEEE, Vol.

60, No. 2, Feb. 1972.

64. Nuese, C.J., Kressel, H., Ladany, I., “Solid State: The Future for LED’s,”

IEEE SPECTRUM, Vol. 9, No. 5, May 1972.

65. Maruska, H.P., Stevenson, D.A., Pankove, J.I., “Violet Luminescence of

Mg-Doped GaN,” APPL. PHYS. LETT., Vol. 22, No. 6, March 1973.

Diodes,” J. LUMINESCENCE, Vol. 5, No. 1, March 1972.

Diodes,” RCA REVIEW, Vol. 32, No. 3, Sept. 1971.

68. Pankove, J.I., Miller, E.A., Berkeyheiser, J.E., “GaN Yellow-Light

Emitting Diodes,” J. LUMINESCENCE, Vol. 6, No. 1, Jan. 1973.

69. Pankove, J.I., “‘UV dc Electroluminescence from GaN,” J. LUMI-

NESCENCE, Vol. 5, No. 6, Dec. 1972.

Back

145

Section 10

Detector Characteristics

There are two general classes of photodetectors; photoemissive devices in which photoelectrons are emitted into a vacuum or gas, and solid-state devices in which the excited charge is transported within the solid by holes or electrons. Detectors utilizing photoemission are principally vacuum photodiodes, gas-filled phototubes, and photomultipliers. Solid-state detectors are available in a wide variety. These devices may be classified as photoconductive or photovoltaic types. Typical solid-state detectors are p-n junction photocells, p-n-p phototransistors, avalanche photodiodes, p-i-n photodetectors, and Schottky-barrier devices.

Although most non-critical applications can use any of these photodetectors there are some applications in which certain devices are particularly suitable.

Vacuum photodiodes are used in applications where a relatively large sensitive area may be required, oil burner flame monitoring being a typical example.

Vacuum photodiodes are also used as the sensor in spectrophotometers. Some vacuum photodiodes which have been specially designed to have a rise time in the order of 30 ps are of use in laser applications where the radiation level is quite high. Gas-filled phototubes were originally used in large numbers as the detectors of motion-picture sound. The gas filling provides an amplification factor of 5 to 10 but limits the speed of response to that just adequate for the audio range.

146

Electro-Optics Handbook

Photomultiplier tubes are manufactured in a wide variety of designs. This type of detector, utilizing either conventional secondary-emission dynodes or microchannel plates, is generally most useful in applications where radiation levels are very low and high speed of response is required. The secondary-emission gain factor of a photomultiplier may be as high as 107.

This high gain permits the signal to exceed the noise components of the output and amplifier circuit so that the limitation to detection becomes the statistical variation in the photocathode current. Photomultiplier tubes are widely used in scintillation counting applications, including the medical

“gamma” camera, and in astronomy, laser ranging, and spectroscopy.

Solid-state photodetectors are used in a variety of applications. Inexpensive

CdS photoconductive cells are used in street-light controls, oil-burner controls, and exposure controls in photography. The silicon photovoltaic cell is well known for its use as a solar energy converter. Other types of silicon p-n junction photocells are used in sound-on-film pickup, card reading, and in a variety of industrial controls. The silicon photodetector is small, reliable, and has high quantum efficiency through the visible to near infrared. Silicon avalanche detectors are characterized by high gain and fast speed of response; they find use in laser ranging. A number of solid-state photocells have been developed for detection of radiation in the near and far infrared. In the near infrared, materials such as PbS and Si are useful. Photodetectors for use in the far infrared must be cooled. Cells of this type are (HgCd)Te, InSb, PbSe,

Ge:Au, Ge:Hg, and Ge:Zn.

10.1 FUNDAMENTAL PHOTODETECTOR RELATIONSHIPS AND

DEFINITIONS

Because of the differing nature of the various types of photodetectors, it is not possible to characterize all of them in identical terminology. Although the units of measurement may differ, there are some characteristics that are common to all devices: spectral response, speed of response, and limits of detectivity.

Figure 10-l is a glossary of the more common parameters, symbols, and units.

Incident Flux

- The response of a photodetector is evaluated in terms of the flux incident on the sensitive area of the detector, The flux may be specified as the number of quanta per second at some wavelength, the radiant flux in a narrow wavelength band, the radiant flux over a wide band of wavelengths, luminous flux, and in some cases as a density, flux per unit area, in the plane of the device aperture or surface.

Detector Characteristics

Parameter

Signal Response

(the symbol S is commonly used as a lower case subscript to denote signal current, signal voltage, etc.)

Symbol

S

Relationship Between Quanta and Radiant Flux Units -

The energy of a single quantum is hv quency and wavelength of the radiation, and c is the speed of light. The length band may be converted to a rate of flow of quanta

N= hc

(in quanta per second)

(10-l)

Equivalent Luminous Flux

- As noted in Section 5, the ratio of luminous

Electro-Optics Handbook

Thus

(in lumens) (10-2)

Responsivity and Signal Current

- The term responsivity (R) is used to describe the sensitivity of the photosensor and is the ratio of the output current or voltage to the input flux in watts or lumens. When the responsivity

(10-3)

If R is given in amperes per lumen, the signal current is given by

(10-4)

Sometimes, the radiant flux is shown for a band of wavelength, viz.,

(10-5)

In this case the responsivity has a different although the form of the equation remains value in terms of amperes/watt

(10-6)

Quantum Efficiency photoelectron is emitted (or one electron-hole pair is generated) for each incident quantum. (Note: In a consideration of the fundamentals of the reaction between radiation and photodetector, quantum efficiency is sometimes defined in terms of absorbed rather than incident quantum; however, from the standpoint of the user, it is the incident quantum that is of interest). Quantum efficiency is usually defined at a particular wavelength.

Detector Characteristics

Thus,

Number of photoelectrons per second

Number of incident quanta at wavelength

The number of photoelectrons per second is given by

149

(10-7) where e is the charge of the electron and the number of quanta per second is given by equation 10-l. Therefore, the quantum efficiency is given by

(10-8)

When the values of Figure 3-1 are used, the value of the constant hc/e is

(10-9)

Accordingly,

It is to be noted that quantum efficiency generally refers to the primary process in the device; i.e., the interaction of the incident radiation and the primary photosensor. In some cases where the responsivity is recorded, a gain mechanism is included in the device between the prime photosensor and the output as, for example, in a photomultiplier or avalanche photodiode.

However, very little advantage is achieved by referring to a quantum efficiency which includes the gain and which, therefore, may be many times unity.

Dark Current

- Dark current is that current that flows in a photodetector in the absence of signal and background radiation. The average or DC value of

150

Electro-Optics Handbook

Noise

Current

- There are various sources of noise or current fluctuation which interfere with the precise measurement of the signal current. Dark current has a random fluctuation as does signal current. When the individual pulse can be observed, these fluctuations are manifest in the random arrival of the dark or signal pulses. Sometimes, the noise in the associated components, such as thermal (or Johnson) noise in the coupling resistor or amplifier noise, is dominant.

Signal-to-Noise Ratio

- Usually the signal-to-noise ratio (S/N) is expressed in terms of the noise in a particular bandwidth. It may be expressed in decibels or, in photoelectron counting applications, as the ratio of a number to the standard deviation of the number in a particular count duration.

Equivalent Noise Input

- The Equivalent Noise Input (ENI) is defined as that value of input flux that produces an rms signal current that is just equal to the rms value of the noise current in a specified bandwidth (usually 1 Hz).

Other parameters such as frequency, the type of light modulation, and temperature should also be specified. Equivalent noise input characteristics are useful in determining the threshold of detection in equivalents of the input flux in watts or lumens.

Noise Equivalent Power -

Noise equivalent power (NEP) is essentially the flux in watts incident on the detector which gives a signal-to-noise ratio of unity. The frequency bandwidth and the frequency at which the radiation is chopped must be specified as well as the spectral content of the radiation.

The two most common spectral specifications are for total radiation from a black body whose temperature is 500 K or monochromatic radiation at the peak of the detector response.

Detectivity is a figure of merit providing the same information as NEP but describes the characteristics such that the lower the radiation level to which the photodetector can respond, the higher the detectivity.

specification and that NEP is normally specified for a bandwidth of one hertz, the two forms of NEP are numerically equal. However, in this handbook, NEP is taken as originally defined by R. Clark Jones (References 70 and 71); it has no bandwidth in its units although NEP may be a function of noise bandwidth as well as temperature and test frequency.

Detector Characteristics 151

Specific Detectivity

- Because the NEP for many types of IR photodetectors is proportional to the square root of the sensitive area (A) and to the square root of the bandwidth (B) of the measuring system, a specific detectivity

(D*j has been defined which permits a comparison of sensors of different areas measured in different bandwidths.

(10-10) or

10.2 SPECTRAL RESPONSIVITY AND SPECIFIC SPECTRAL

DETECTIVITY

The relative spectral response characteristics of a number of photodetectors have been standardized by the EIA (Electronics Industries Association).

These responses have been assigned S-designations, e.g., S- 1, S- 11, S-20.

Figure 10-2 lists some of the S-designation responses as well as many other spectral responses. Other typical characteristics in this figure have been taken mainly from References 72 and 73.

UV-Visible Spectral Responses for Photoemissive

- Figure 10-3 responsivity. Generally, the lower-limit cut-off wavelength of most photoemitting cathodes is established by the transmission characteristics of the window material and to some extent by the thickness of the photocathode layer for transmission-type photocathodes. The spectral transmittance of several commonly used window materials is given in Section 12.

Visible Light Spectral Responses for Photoemissive Devices

- Figure 10-4 gives the spectral responsivity curves for photoemitters that are most useful for detecting radiant flux in the visible region of the spectrum. Other responses having good sensitivity to visible light are shown in Figure 10-3 and

10-5.

Near-Infrared Spectral Responses for Photoemissive

Devices - Figure 10-5 shows those photoemitters having responsivity that extends usefully into the

I

I

Spectral

Response nation

Photo-

S-8

S-9

S-10

S-l 1

S-l

S-3

S-4

S-5

S-13

S14

S-16

Type of

Sensor

Photoemitter

Photoemitter

Photoemitter

Photoemitter

Photoemitter

Photoemitter

Photoemitter

Photo emitter

Photoemitter

P-n

Alloy

Junction

Polycrystalline

Photoconductor

Opera- Maximum Luminous

Window Response

Material

Mode* Wavelength Photoof of Typical Typical cathode nm

800 .

Lime T,R

Glass

Lime R

Glass

Lime R

Glass

9741 R

Glass

Lime R

Glass

7052 T

Glass

Lime T

Glass

Lime T

Glass

Fused T

Silica

Lime -

Glass

420

400

340

365

480

450

440

440

1,500

Lime -

Glass

730

m

S-17

S-19

S-20

Not

Cs-Sb

Cs-Sb

Na-K-Cs-Sb

Na-K-Cs-Sb

(ERMA III)

Photoemitter with

Reflective

Substrate

Photoemitter

Photoemitter

Photoemitter with

Reflective

Substrate

Photoemitter

Lime

Class

Fused

Silica

Lime

Glass

Lime

Glass

7740

Pyrex

R

R

T

R

T

490

330

420

530

565

125

40

150

300

230

83

65

6 4

89

45

21

24.4

18.8

20.8

10

S-21

S-23

S-24

S-25

Not

Standardized

Cs-Sb

Rb-Te

K-Na-Sb

Cs-Te

Photoemitter

Photoemitter

Photoemitter

Photoemitter

Photoemitter

Photoemitter

Photoemitter

9741

Glass

Fused

Silica

7056

Glass

Lime

Glass

Lime

Glass

Lime

Glass

Fused

Silica

T

T

T

T

T

R

T

440

240

380

420

380

400

250

-

30

45

200

85

-

65

23.5

4

67

4 3

97

54

1 5

6.6

2

21.8

12.7

31

17

7.4

* T = Transmission Mode R = Reflection Mode

Fig. IO-2 Spectral response designations and related characteristics. (Part I

of

2)

1.2

1.4

4

0.001

0.0003

l-

0.02

-

-

0.3

0.3

-

Not

A

Standardized f

Ga-As

Ga-As-P

Ga-In-As

Cd-S

Cd( S-Se)

Si

Si

* T = Transmission Mode

Photoemitter

Photoemitter

9741

Glass

9741

Glass

R

R

Photoemitter

9741

Glass

Lime -

Glass

R

Polycrystalline

Photoconductor

Polycrystalline

Photoconductor

Lime -

Glass

N-on-p ’ No -

Photovoltaic

Window

P-i-n

Photoconductor

Lime -

R = Reflection Mode

830

400

400

510

615

860

900#

300

160

100

-

-

620#

57

-

68

45

-

580.

17.6

-

10

14

-

0.1

0.01

-

-

-

85# l

Photovoltaic short-circuit responsivity

Fig. 1 O-2 Spectral response designations and related characteristics. (Part 2 of 2)

Detector Characteristics

, I I

I

QUANTUM EFFICIENCY = 10 %

\

I

155

1

100 200 300 400 500

600 700 800

UV-visible photoemitter characteristics. Absolute spectral responsi-

vity of various photocathode-window combinations useful in the

ultraviolet-visible region of the spectrum

Long-Wave Threshold Variation with Temperature for Photoemissive Devices-

The long-wavelength threshold of certain photoemitters is a function of temperature and decreases as the temperature of the photoemitter decreases.

Figure 10-6 shows this effect for four typical photoemitting materials (See

Reference 74). These photocathodes, which extend into the near infrared, are normally cooled to reduce dark current and noise. Note that no decrease in long wavelength threshold was observed for the S-l spectral response.

Visible and Near-Infrared Spectral Responses for Solid-State Devices number of common photoconductive and photovoltaic cells. The n-on-p diffused silicon and Se photovoltaic characteristics represent typical responsivities under short-circuit conditions. The p-i-n silicon photoconduc-

Relative spectral response characteristics for CdS and CdSe are shown in

156

Electro-Optics Handbook

Fig. 10-4 Visible photoemitter characteristics. Absolute spectral responsivity of various photocathode-window combinations usefil for the detection of visible light.

Far-Infrared Spectral Responses for Solid-State Devices

- When a far-infrared response is required, solid-state detectors must be used. No photoemissive

Photoconductive materials can be made having excitation energies corre-

Detector Characteristics

Go-As + 9741 GLASS

WAVELENGTH (

A

) - nm

Fig. 10-5 Near infrared-visible photoemitter characteristics. Absolute spectral responsivity of various photocathode-window combinations useful for the detection of visible and near infrared radiant flux.

sponding to tenths and even hundredths of an eV. However, such materials require cooling to prevent thermal excitation from obscuring the signal.

The spectral response characteristics of the far-infrared solid-state detectors of Figures 10-8 and 10-9 are shown in terms of specific detectivity, D*. The

158 Electra-Optics Handbook

+ 7740 GLASS

Go-As +

9741 GLASS

200 400 600 800 1000 1200 1400

00

0-6 Typical effect of photocathode cooling using four

photocathode materials.

typical

data are taken from references 25 and 75. The particular temperature at which each response characteristic was measured is indicated on the Figures.

The dashed curves represent the limitation on specific detectivity imposed by the fluctuation of the background thermal radiation (assumed to be

Detector Characteristics 159

1.2

1.4

1.6

1.8

2.0

detectors.

sensor can only equal these theoretical curves if each quantum received is detected.

) with Temperature and Modulation Frequency -

Figure 10-10, which supplements the spectral response characteristics of detectivity for various solid-state photodetectors. The particular value for D* is taken at the wavelength of maximum spectral detectivity. Figure 10-l1 as a function of radiant flux modulation (chop) frequency for PbS.

160

100

80

Electro-Optics Handbook

0.8 1

10.3 NOISE

Photodiodes -

Devices such as a vacuum photodiode or a silicon p-n photodiode produce a noise current variation of the output current which ultimately limits the detectivity of the device in the absence of other may be defined as follows:

(10-l1) where

e = the charge of the electron

I = the total average current from the device (the sum of the signal

B = the bandwidth

Detector Characteristics

295KBACKGROUNDTEMPERATURE

161

II I lllll

I i

.O

1.5

2.0

2.5

4

5 6

7

WAVELENGTH (A) -pm

8 9 1 0 1.5

2 0 2 5 3 0

Fig. 10-8 Spectral detectivities for above-average thin-film detectors at jkequency fm

(courtesy Santa Barbara Research Center).

162

Electra-Optics Handbook

1 .o

1.5 2.0

2.5 3 4 5 6

7 8 9 ‘0 15 20 25 30 40

Fig. 10-9 Spectral detectivities for above-average crystal detectors at frequency fm (courtesy Santa Barbara Research Center).

In summing the three components of the total average current I, it is assumed that each component is statistically independent of the other so that the noise components may be added by taking the square root of the sum of the squares.

Detector Characteristics

LIQUID

STERADIANS FIELD OF VIEW

.BACKGROUNDTEMPERATURE

163

180 200

DETECTOR TEMPERATURE (T) -K

220 240

260 280

Fig. 1 O-l 0 Typical dependence of specific detectivity on operating temperature (courtesy Santa Barbara Research Center).

detectors (courtesy Santa Barbara Research Center).

164 Electro-Optics Handbook

tions involving low light levels, the noise in the photodiode output (equation

10-l1) may be totally obscured by other sources of noise such as that of the amplifier used as the measuring instrument. In such a case, the total detectivity capability of the diode is not used. To overcome this difficulty, devices such as photomultipliers have been developed in which the primary photocurrent is amplified within the device itself. Although this amplification is not noise free, it adds in most cases only a small increment to the fundamental diode output noise compared to the amplified signal current.

The rms shot-noise current at the output of a photomultiplier is given by

(10-12) where

:he

B = the bandwidth the total gain of the photomultiplier e = the charge of the electron

Note that the inherent noise in the photocathode gain of the photomultiplier as is the signal current.

is multiplied by the total

An additional factor to be considered is the statistics of secondary emission of the dynodes. The major contributor is the secondary emission from the assuming Poisson statistics for the secondary emission process. In general, noise values for photomultipliers are somewhat higher than those obtained from equation 10-12. See Reference 76. If the secondary emission of each approximate expression

(10-13)

Detector Characteristics 165

For typical secondary emission gain of 4, the increase in rms noise current over that of a “perfect” amplifier is about 15%.

Photodetectors with Internal Amplification (Avalanche Photodiodes) -

The avalanche photodiode is a p-n junction type photodetector that is operated at the high reverse bias voltages required for avalanche multiplication. Very high multiplication factors M can be achieved, but the process is noisy.

The gain is a result of holes and electrons being accelerated within the depletion layer of the diode; ionization takes place and gain process may be repeated many times. McIntyre (See Reference 77) has analyzed this statistical process and has shown that when the ionization rates for electrons and holes are the same, then the rms noise current (i n n

(at high frequencies) is given by the expression

(10-14) where

M = the multiplication factor e the charge of the electron

= the total average current before multiplication

B = the bandwidth

Note that the noise increase factor over that of a noise-free amplification

Circuit Noise -

When a photodetector is coupled to a circuit, the noise introduced by the circuit elements must be considered. For example, if the noise generated in the resistor must be added to the photoelectron shot noise.

The adding process must be done using the equivalent expression of power, i.e., the sum of the squares of the noise currents or of the noise voltages. The total rms noise is then obtained by taking the square root of the sum. For a coupling resistor, the thermal rms noise voltage developed is given by

(10-15) where k = Boltzmann’s constant

T = absolute temperature

B = the bandwidth

166

Electra-Optics Handbook

The equivalent thermal noise current may be written

(in amperes) (1016)

When the photodetector is coupled to an amplifier, the equivalent rms noise current expressed in terms of current through the coupling resistor is given by

(10-17)

3 where

RL= the resistance of the coupling resistor in ohms

Rt = the equivalent noise resistance of the amplifier input in ohms the total capacitance of the tube and associated input in farads

(See Reference 77)

B = the bandwidth

Pulse Counting Applications -

Operation of the photomultiplier in a pulse counting mode is of growing importance. When the photomultiplier is used to count single electron pulses first with radiation incident on the photocathode and then with radiation excluded from the photocathode, it becomes important to determine the optimum time to be spent under each condition to provide the best signal-to-noise ratio.

radiation incident on the phototube

Detector Characteristics

167

represent the respective count durations. With the tube irradiated, the total in the signal determination becomes

Accordingly, becomes the expression for signal to noise for this counting process

(1049)

Figure 10-l 2, which is a plot of equation 10-20, shows the optimum fraction of the count time that should be spent for the dark count as a function of the count time and dark count time should be equal.

However, if the signal count in the light dominates, then the time for measuring the dark count may be reduced significantly.

10.4 TIME CHARACTERISTICS OF PHOTODETECTORS

Time Response Characteristics of Photomultipliers

- The three basic parameters which define a photodetector are its responsivity, noise, and temporal response characteristics. The limitation in speed of response for

Electro-Optics Handbook

0.6

-

0 . 1

0

1 10 100 1000 10000

Fig. 10-12 Fraction of the count time to be used for the dark count to obtain the optimum signal-to-noise ratio for a fixed total time.

photomultipliers is principally one of design, i.e., the structural design of the

“front end” (photocathode-to-first-dynode region), the electron multiplier, and the anode output structure. The time response capability of the photomultiplier is usually defined in terms of the anode output pulse characteristics for delta-function photocathode excitation. Scintillation and

“photon” (properly photoelectron) counting systems are examples of natural occurrences of delta-function light excitations. In practical test measurements, pulsed LED’s, mode-locked lasers, and spark sources are often used to approximate the delta-function light source.

The most commonly specified anode pulse characteristics are rise time, fall time, and FWHM (Full Width at Half Maximum). These characteristics are shown in Figure 10-13. Measurement techniques on these and other time characteristics of photodetectors are contained in References 78,79, and 80.

Time Response Characteristics of Solid-State Photodetectors

- Rise time is the most commonly specified temporal figure of merit for solid-state detectors. The measurement is quite similar to that used for obtaining rise time of the photomultiplier except a step-function light excitation is employed.

Detector Characteristics 169

(FWHM).

The speed with which a solid-state photodetector responds to radiant signals is determined ultimately by the time it takes for the generated electrons and holes to be collected in the diode. Best time response is attained by using fully depleted detectors to eliminate any series resistance, and very small loads, e.g., 50 ohms. When higher value loads are used, the speed of response is limited by the RC time constant of the circuit. If the circuit is carefully constructed and the amplifier that follows it has negligible input capacitance, the capacitance of the photodiode limits the speed of response of the system.

The speed of response of the circuit may be described in two ways. First, the radiation can be modulated sinusoidally and the frequency of modulation increased until the output signal power falls to l/2 of its low-frequency value

170 Electro-Optics Handbook

photodetector can be irradiated with a step input of radiant flux, and the rise time (t r

) of the detector can be measured. (Rise time is the time between the

10% and 90% points of the output waveform). These two methods are equivalent and are related to a first order of approximation as follows

(10-21) where and

(10-23)

10.5 SOURCE-DETECTOR MATCHING

It is often desirable to determine the response of a photosensitive device to a particular source of radiation. Narrow spectral band sources (e.g. lasers) are easily accommodated using the spectral response data already presented.

However, wide spectral band sources of radiation require evaluation of an integral like that shown in Figure 10-14. The responsivity values in that table are the results of such integrations carried out for several representative sources and for a variety of photoconductors and photoemitters.

References

25. INFRARED COMPONENTS, Brochure No. 67CM, Santa Barbara

Research Center, Goleta, Ca., 1967.

39. Schwartz, M., INFORMATION TRANSMISSION, MODULATION, AND

NOISE, McGraw-Hill Book Co., New York, N.Y ., 1959.

70. Jones, R-C., “Phenomenological Description of Response and Detecting

Ability of Radiation Detectors,” PROC. IRE, Vol. 47, No. 9, Sept. 1959.

71. Marton, L., Editor, ADVANCES IN ELECTRONICS, Academic Press,

New York, N.Y., 1953.

172 Electro-Optics Handbook

72. Engstrom, R.W.,

“Absolute Spectral Response Characteristics of

Photosensitive Devices,” RCA REVIEW, Vol. 21, No. 2, June 1960.

73. Engstrom, R.W., and Morehead, A.L., “Standard Test-Lamp Temperature for Photosensitive Devices - Relationship of Absolute and Luminous

Sensitivities,” RCA REVIEW, Vol. 28, No. 3, Sept. 1967.

74. Cole, M. and Ryer, D., “Cooling PM Tubes for Best Spectral Response,”

ELECTRO-OPTICAL SYSTEMS DESIGN, Vol. 4, No. 6, June 1972.

75. SBRC WALL CHART 3M67, Santa Barbara Research Center, Goleta, Ca.,

1967.

76. RCA PHOTOMULTIPLIER MANUAL, Technical Series PT-6 1, 1970.

77. McIntyre, R-J., “Multiplication Noise in Uniform Avalanche Diodes,:

IEEE TRANS. ON ELECTRON DEVICES, Vol. ED-13, No. 1, Jan. 1966.

78. McHose, R-E., “Fast Photomultiplier Tube Techniques,” RCA Application Note AN-4797, 1971.

79. McHose, R.E., “Time Characteristics of Photomultipliers - Some General

Observations,” RCA Application Note AN-4884, 1972.

80. METHODS OF TESTING PHOTOMULTIPLIERS FOR SCINTILLA-

TION COUNTING, IEEE Standard No. 398,1972.

81. Jamieson, J.A., et al, INFRARED PHYSICS AND ENGINEERING,

McGraw-Hill Book Co., New York, N.Y., 1963.

82. RCA PHOTOTUBES AND PHOTOCELLS, Technical Series PT-60, 1963.

83. RELATIVE SPECTRAL RESPONSE DATA FOR PHOTOSENSITIVE

DEVICES (“S” CURVES), JEDEC Publication No. 50, Oct. 1964.

84. TYPICAL CHARACTERISTICS OF PHOTOSENSITIVE SURFACES,

JEDEC Publication No. 61, Dec. 1966.

85. IRE STANDARDS ON ELECTRON TUBES - METHODS OF TESTING,

IEEE 62, IRE-7.S 1, 1962.

Back

173

Section 11

Image and Camera Tubes

This section presents a basic comparison of the general characteristics of the different types of image and camera tubes. Guide lines for low-light-level operation and statistical limitations to viewing are also discussed.

11 .l IMAGE TUBES

An image tube (often called an image-intensifier or image-converter tube) is an electron device that reproduces on its fluorescent screen an image of the radiation pattern focused on its photosensitive surface. These tubes are used when it is desired to have an output image that is brighter than the input image or to convert non-visible radiation from an image into a visible display.

The image tube consists basically of a photocathode upon which a radiant image is focused, an electron lens, and a phosphor screen upon which the output is displayed. Image intensification results when the electrons emitted by the photocathode strike the phosphor screen after being accelerated by high voltage. Luminance gains in a single-stage image tube are usually in the order of 50 to 100. When image tubes are coupled, it is possible to obtain to 106. With such gains it is possible to make observations that are limited by photoelectron statistics only.

The several different families of image tubes which have been developed can be categorized by the type of electron-optical focusing mechanism. In an electrostatic-type image tube, Figure 11-1, an electrostatic field directs the photoelectrons through an anode cone and focuses an inverted image on the

174

CATHODE

CONTACT

Electro-Optics Handbook

ANODE

AND FOCUSING

VIEWING

LENS

ERECT

IMAGE

FOCUSING

SCREEN

Fig. 11-1 Schematic diagram of an electrostatic-type image tube.

phosphor screen. Electrostatically focused image tubes are relatively simple to operate requiring only a suitable optical lens for focusing the scene on the photocathode, an ocular for viewing, and a power supply. These tubes frequently use a fiber optic faceplate to minimize the fall off in image resolution toward the edge of the tube. The fiber optics also permit efficient coupling to another image tube, to a camera tube, or to photographic film.

Although image tubes have, at times, been coupled by conventional optics, the efficiency loss is quite severe.

Another class of image tube may be identified as a “proximity focus” type.

In such a tube, the photocathode and the phosphor screen are in parallel planes spaced closely together. The photoelectrons are not actually focused in this arrangement but, because of the high field between the screen and cathode, do not deviate much from trajectories that are parallel to the tube’s axis. The tube is small and the screen image is erect, but resolution is not as good as that for the electrostatic or magnetic types.

The magnetic-type image tube combines an electrostatic field with an axial magnetic field provided by either a solenoid or a permanent magnet. With a uniform magnetic field, the resolution is good over the entire screen and distortion effects are very low. Magnetic-type image stages are normally coupled by means of a thin mica or fiber-optic layer with a phosphor on one side and a photocathode on the other, all within the same vacuum. Figures

11-2 and 11-3 show the construction techniques of typical three-stage electrostatically focused and magnetically focused image intensifier tubes.

Image and Camera Tubes

175

Fig. 11-2 Schematic diagram of typical three-stage electrostatically focused image tube.

GLASS OUTPUT

THIN MICA

INTERSTAGE

COUPLERS

Fig. 11-3 Schematic diagram of typical three-stage magnetically focused image tube.

So-called “second generation” image tubes make use of microchannel plates

(MCP’s) to achieve luminance gains in the order of 104. Although high gain is achieved in a small space by means of the MCP structure, the pulse height statistics of the image are degraded by the inherent fluctuation of noise from the MCP. The MCP is essentially a thin secondary-emission current amplifier located between the photocathode and the phosphor screen. This amplifier makes possible a high-gain tube having not only minimum size and weight, but also a saturable-gain characteristic which minimizes blooming (or halation) effects. The microchannel plate itself consists of parallel array of length. The inside walls of the cylinders are coated with a secondary emitting material. Primary electrons strike the inside walls near the entrance end and cause secondary electrons to be emitted. These secondary electrons in turn

176 Electro-Optics Handbook

strike the wall further into the depth of the cylinder and create additional secondary electrons. This cascading mechanism produces the high gain. There are two distinct designs of image tubes utilizing the MCP’s: the “wafer” design and the inverter design. These tubes are illustrated in Figures 11-4 and

11-5. Most image tubes are also differentiated by the nominal useful diameter of the photocathode. Typical diameter values are 18, 25, and 40 mm.

f

MICROCHANNEL

PLATE

VIEW

OUTPUT

OUTPUT

FIBER OPTICS

Fig. 11-4 Schematic diagram of proximity focus image tube of the “wafer” design utilizing an MCP to increase gain.

ELECTROSTATIC

LENS

MICROCHANNEL

PLATE

Fig. 11-5 Schematic diagram of electrostatic-focus type image tube utilizing an MCP to increase gain.

11.2 CHARACTERISTICS OF IMAGE TUBES

The resolution capability of magnetically and electrostatically focused single-stage image intensifiers is comparable to that of photographic films such as Royal-X Pan or Tri-X Pan. Figure 1l-6 relates typical image tube

Image and Camera Tubes

177

resolution ranges in limiting line-pairs per mm to equivalent TV lines per picture height and to the resolving power of photographic film.

Equivalent TV

Image Tube line/picture Comparable

Limiting Resolution height (25-mm Photographic

(line pairs/mm) Picture Height) Film

25 - 40 1050-2000 ’ t

-

45 - 55 2250 - 2750 -

60 - 70

75 - 90

3000 - 3500

3750 - 4500

Kodak

Resolving

Power

Designation

-

-

Royal-X Pan ML (Medium-Low:

Tri-X Pan M (Medium)

Fig. 11-6 Image tube limiting resolution compared to that of photographic film.

The modulation transfer function (MTF) or the contrast transfer function

(CTF) characteristics are preferable ways of specifying image tube resolution.

Limiting resolution values, commonly specified in image tube data publications, provide only a single point on the MTF or CTF characteristic curve, The measured value of limiting resolution corresponds closely with spatial frequency in line pairs per mm at the 3% contrast point. Figure 11-7 gives the typical MTF characteristics of several image intensifiers.

Most image tube manufacturers measure MTF with a commercially available modulation transfer analyzer. The analyzer projects an image of a narrow slit illuminance falling within the slit is adjusted to provide a fairly bright image on the image tube output screen that is a replica of the slit imaged on the photocathode. The analyzer has an internal optical system that refocuses the intensified slit from the tube screen onto a moving mask whose transmission varies sinusoidially along its length and whose frequency varies from very low

(a fraction of a cycle per millimeter) to about 10 cycles per millimeter. The analyzer measures the amplitude of the spatial frequency components in the modulated output image. The input slit image is also analyzed in the frequency domain and the comparison between the output and input data determines the MTF of the image tube. See Section 8-3 for additional information on the modulation transfer function and on contrast transfer function characteristics.

Electro-Optics Handbook

IMAGE INTENSIFIER

20 -

SPATIAL FREQUENCY - CYCLES/MILLIMETER

Fig. 1 l-7 Typical MTF characteristics of one-stage, two-stage, and three-stage electrostatically focused image tubes (useful screen diameter- 18 mm).

Image and Camera Tubes

179

The gain of an image tube may be defined in a number of ways such as (1) radiant power output divided by radiant power input, (2) luminous flux output divided by luminous flux input, or (3) luminance output divided by illuminance input. The particular gain definition is usually chosen to meet the

0 10 20 30

Fig. 11-8 Typical luminance gain characteristics of image tubes.

180

Electro-Optics Handbook

requirements of the application. Figure 1 l-8 shows luminance gain of singlestage, two-stage, and three-stage 25-mm image tubes as a function of applied voltage.

Image tubes are available with a number of different spectral responses. See

Section 10. The S-l spectral response has been widely used in image tubes for covert viewing at night with an auxiliary infrared radiation source (usually referred to as an active system). Image tubes having a S-20 spectral response and variations of the multialkali photocathode have been used for night viewing without auxiliary irradiation (usually referred to as a passive system) because of their higher quantum efficiency and good response in the red and near-infrared regions of the spectrum.

The output phosphor is usually selected to optimize the tube response by matching to a chosen mode of reception. For example, the P20

(yellow-green) phosphor is frequently used for direct viewing because its spectral output peaks close to the maximum sensitivity of the human eye. See

Section 10 for the typical spectral emission characteristics of various phosphors. The Pl 1 phosphor is used for photographic applications because its peak spectral output (about 460 nm) closely matches the characteristics of most photographic films. The P20 and Pll phsophors in single-stage tubes have a persistence in the order of 10 ms, from initial brightness to the 10 percent decay point, under normal image intensifier operating conditions.

Coupled intensifier stages will, of course, have longer persistence. Because the persistence durations of P11 and P20 phosphors are not suitable for some applications, other phosphors such as P15 and P16 which have a faster decay characteristic are often used. However, these phosphors usually have lower efficiency and a lower resolution than the Pl1 or P20 phosphors.

11.3 TELEVISION CAMERA TUBES

The television camera tube is an electron device which converts an optical image into an electrical signal. Camera tubes are used to generate a train of electrical pulses which represent light intensities present in an optical image focused on the tube.

TV camera tubes are used in commercial TV broadcasting, closed-circuit monitor service, the conversion of motion picture into electrical signals, and low-light-level viewing for military and other surveillance applications. A description of each of the many different types of TV camera tubes follows.

The vidicon is the most widely used camera tube. Its small size and simplicity of operation and adju stment permit its use by relatively inexperienced

Image and Camera Tubes

181

personnel. Vidicons have moderate sensitivity and are useable in many locations without auxiliary lighting. The speed of response of the vidicon, generally, is somewhat less than that of most other types of camera tubes. A schematic representation of a vidicon tube is given in Figure 11-9.

ELECTRON

PHOTOCONDUCTIVE

SIGNAL

OUTPUT

Fig. II-9 Schematic representation of vidicon camera tube.

The vidicon utilizes an electron beam to scan a photoconductive target which is the light sensor. A transparent conductive layer applied to the front side of the photoconductor serves as the signal (target) electrode. The signal electrode is operated at a positive voltage with respect to the back side of the photoconductor which operates at the cathode (near zero) voltage. In operation, the scanning beam initially charges the back side of the target to cathode potential. When a light pattern is focused on the photoconductor, its conductivity increases in the illuminated areas and the back side of the target charges to more positive values. The electron beam then reads the signal by depositing electrons on the positively charged areas thereby providing a capacitively coupled signal at the signal electrode.

The image orthicon is a more intricate camera tube type than the vidicon.

However, it has very high sensitivity and the ability to handle a wide range of light levels and contrasts. A disadvantage of the tube is that the return-beam mode of operation results in excessive noise in the dark areas of the image.

For many years, the image orthicon was used almost exclusively for live pickup in studio and outdoor broadcast television cameras. In recent years the image orthicon has been replaced by certain vidicon types (e.g., the lead oxide types) in such applications.

A schematic representation of an image orthicon is given in Figure 1 l-10. The image orthicon utilizes a photocathode as the light sensor. The photoelectron image pattern developed at the photocathode is focused by an axial magnetic field producing one spiral loop onto a thin moderately insulating target

182

surface. When the photoelectrons from the photocathode strike the target, secondary emission occurs causing the establishment of net positive charges on the target. The electron beam scans the charged target pattern, deposits some electrons on the more positively charged areas, and the modulated beam returns to an electron multiplier surrounding the electron gun. The output signal is the amplified anode current of the electron multiplier.

LIGHT

Fig. 11-l 0 Schematic representation of image orthicon camera tube.

The image isocon is a variant of the image orthicon in which an improved electron-optic system is used and in which the inherent beam-noise problem is largely overcome. The image isocon produces a higher signal-to-noise than the image orthicon, particularly in the dark areas of the picture, and it has equivalent or better resolution, sensitivity, and amplitude response. This tube finds use in low-light-level TV and as a pickup tube for monitoring the output of X-ray image intensifiers in medical applications.

A schematic representation of the image isocon is given in Figure 1 l-l 1. In operation, the image isocon is similar to the image orthicon, although the method of extracting the output signal from the return beam differs. When the electron scanning beam approaches the target, several events occur: electrons may enter the target and neutralize a positive charge, electrons may fail to land and be electrostatically reflected, or electrons may land on the target and be scattered back at various angles. The scattered electrons constitute the signal in the return beam. The reflected electrons are eliminated by means of a carefully aligned baffle positioned to assure separation of the return beam components caused by the different electron paths.

Image and Camera Tubes

PHOTOCATHODE

FIRST DYNODE

OFELECTRON

183

RETURNBEAM

SIGNAL

OUTPUT

Fig. 11-11 Schematic representation of image isocon camera tube.

The

SIT (silicon intensifier target) and the

SEC (secondary electron conduction) camera tubes are similar to the image orthicon in that they both employ a photocathode as the image sensor, but the scanning and read-out methods are more like that of the vidicon. A schematic representation of the

SIT tube and the SEC tube is given in Figure 11-12. In both tube types, the photoelectrons are focused onto a special target which provides relatively high gain before the scanning operation commences. For the SIT camera tube, the target is a very thin silicon wafer upon which a tightly spaced matrix of p-n junction diodes is formed. The center-to-center spacing of the primary photoelectron, accelerated to perhaps 10 keV, impinges on the target and causes multiple dissociations of electron-hole pairs. Gains of

1000 or more may be achieved. The holes are collected at the p-side of the diode where the charge is neutralized by the scanning beam. The signal is read out on the backplate of the target.

PHOTOCATHODE

LIGHT

PHOTOELECTRONS

SIGNAL

OUTPUT

Fig. 1 l-l 2 Schematic representation of SIT and SEC camera tube.

184 Electro-Optics Handbook

The target of the SEC camera tube is a thin layer of semiporous KC1 which has the property of providing gain by internal secondary electron emission.

Typical electron gain figures obtained are as high as 100. The signal is read out, like that of the SIT tube, from the backplate of the target.

Both the SIT and SEC tubes have been used extensively for low-light-level pickup. The SIT tube is capable of a very wide range of operation because of the flexibility of its gain mechanism. For example, ,a SIT tube was successfully used as the color camera tube in the last Apollo moon missions.

When an image intensifier is coupled to the SIT tube, the combination is capable of photoelectron-noise-limited operation at the very lowest light levels.

The image dissector is a non-storage type of camera tube in which a photocathode is used as its light sensitive surface. This tube, illustrated schematically in Figure 11-13, does not employ a scanning beam. In the image dissector electron streams from the illuminated photosurface are focused onto an image plane. A set of deflection coils provides fields which sweep the entire electron image, in TV fashion, across an aperture positioned near the center of the image plane. An electron multiplier behind the aperture multiplies only those electrons passing through the hole. The electrons from the output of the multiplier are the output signal. Those electrons not passing through the aperture are discarded. Although the image dissector has low efficiency, because of its very rapid response it is used in application such as star trackers, photon counters, and document readers. If the number of picture elements is small, the lack of storage capability is not too important.

LIGHT

APERTURE

A

SIGNAL

OUTPUT

NOTE: MAGNETIC FIELD CAUSES

DEFLECTION SCANNING

Fig. 11-13 Schematic representation of image dissector camera tube.

A charge-coupled device

(CCD) is an MOS-type solid-state imaging device which requires no scanning beam. A schematic representation of the CCD is given in Figure 11-14. Individual cells are formed into a TV-type raster by an

Image and Camera Tubes

185

array of parallel conducting strips in one direction and p+-type channel stops at right angles. Electron-hole pairs are created when light is incident on the p-type silicon. The charges, representing pictureelement signals, are stored in potential wells under depletion-biased electrodes. The charges are transferred by applying a positive pulse to the adjacent electrodes. The whole image is transferred, in this manner, to a storage raster during the vertical blanking period. Each horizontal line is then read out from the storage raster in sequence in a similar manner to provide the output TV signal.

HORIZONTAL OUTPUT

REGISTER

OUTPUT

AMPLIFIER

LIGHT

INPUT

Fig. 11-14 Schematic representation of CCD (Charge-Coupled Device), a solid-state imager.

The foregoing material provides a basic description of the generic types of camera tubes and devices. Many of these tubes, however, are referred to by trade names. Figure 11-15 identifies the names of the various types currently in use in the camera tube industry.

Figure 1 l-16 is a comparison of some of the more common types of camera tubes and their more important characteristics.

11.4 RESPONSIVITY

Camera tubes are generally rated in terms of output current for a given light level or radiation input level. This quotient, output current divided by incident flux, is called responsivity and varies widely for the different types of camera tubes. The responsivity of vidicons is relatively low because there is no internal gain mechanism as there is in most other camera tube types.

Figure 11-17 shows typical signal output characteristics as a function of faceplate illuminance (also known as a transfer characteristic). The slope of

186 Electro-Optics Handbook

EBS

[SEC

Isocon

[SIT

IV

12V

Name

EBIR

Ebitron

Epicon

Esicon image Isocon

Generic Type

Description

-

Electron Bombardment Induced

Response. A recently proposed acronym describing target action in response to electron excitation (as opposed to photon). In general, this is the target action encountered in tubes of the image orthicon generic class.

Image Orthicon Trade name for EM1 (England) camera tube described by them as an intensifier vidicon. It employs a photocathode, an

“electron bombardment induced conductivity” (EBIC) target and the electron gun structure of a vidicon. As such it resembles the SIT or SEC type of tube.

Image Orthicon Westinghouse Silicon-Intensifier Target

(SIT) tube. (Electron Bombardment

Silicon).

Vidicon

Trade name for General Electric

Silicon Target Tube.

Image Orthicon

Trade name for a Thomson-CSF

(France) tube similar to the SEC.

Image Orthicon A very low noise, high performance tube derived from the Image Orthicon.

Image Orthicon Westinghouse-a SEC tube (see SEC) coupled to an image tube.

-

See Image Isocon.

Image Orthicon

RCA Silicon-Intensifier Target tube

(see SIT) with a coupled image tube.

Vidicon

Vidicon

Vidicon with a coupled image tube.

Vidicon with a 2-stage coupled image tube.

Fig. 1 l-15 Trade names and generic identification of various camera tubes.

(Part I of 3)

Image and Camera Tubes

187

Name

Leddicon

Oxycon

Plumbicon

Proxicon

Rebicon

Resistron

Return Beam

Vidicon

SIEBIR

SEC

SEM

Sidicon

Generic Type Description

Vidicon

Vidicon

Vidicon

Trade name for EEV (English Electric

Valve) lead-oxide vidicon.

Trade name for GEC (General Electrodynamics Corp.) lead oxide vidicon.

Registered trade name for Philips leadoxide vidicon.

Image Orthicon

Trade name for Westinghouse proximity focus SEC tube (see SEC).

Vidicon

Vidicon

Trade name for RCA “return beam” vidicon (see Return Beam).

Trade name for Siemens (Germany) vidicon.

Vidicon

RCA-a vidicon in which the output signal is the returning scanning beam

(present in any Vidicon) which has been amplified by a secondary emission

(multiplier) structure within the tube.

-

Silicon Electron Bombardment Induced

Response. EBIR action involving a silicon target.

Image Orthicon Westinghouse-Secondary Electron

Conduction (referring to storage target mechanism). The SEC is generically an image orthicon using a target fabricated from KCI.

Image Orthicon

Toshiba-Silicon Electron Multiplication.

The tube is similar to the RCA SIT tube.

Vidicon

Trade name for EEV (English Electric

Valve) silicon target vidicon.

Fig. 1 l-15 Trade names and generic identification of various camera tubes.

(Part 2 of 3)

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Electro-Optics Handbook

SIT

Name

ST-Vidicon

Sivicon

Spectraplex

Super Esicon

Tivicon

Vistacon

Generic Type

Description

Image Orthicon

Vidicon

Vidicon

Vidicon

Image Orthicon

Vidicon

Vidicon

Charge Coupled

Device (CCD)

RCA-Silicon Intensifier Target.

Generically an image orthicon.

Electrons emitted by the photocathode are accelerated by high-voltage, focused on a silicon target where the high energy is translated into a large quantity of charged particle pairs and stored by the silicon diode array.

Useful target gains of about 2000 are possible.

Trade name for RCA Silicon Target vidicon.

Trade name for Amperex Silicon

Target vidicon.

Trade name for RCA color vidicon

(three color tube).

Trade name for Thomson-CSF (France) tube consisting of an Esicon coupled to an image intensifier. Similar to ISEC.

Trade name for Texas Instrument

Silicon-Target vidicon.

Trade name for RCA lead-oxide vidicon.

A solid-state charge-coupled camera device.

Fig. 1 l-1.5 Trade names and generic identification of various camera tubes.

(Part 3 of 3)

(1) 1 lux = 0.0929 footcandle

(2) llluminance range on the faceplate for a 50: 1 (34dB) signal range. Details may be observed in the total range.

(3) Illumination from a tungsten lamp, 2856 K color temperature.

(4) Measured at the indicated typical signal level.

(5) Dark current is equivalent to 10% of the signal current.

Dark current is uniform and independent of temperature.

(6) There is a useful compression of the signal above the knee for wide variations of scene luminance.

(7) Larger than the signal current and increases with excess beam current.

Fig. II-16 Important performance characteristics of typical camera tubes.

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Electro-Optics Handbook

the characteristic on a log-log plot is referred to as the “gamma” of the tube type. In some cases, a low gamma has the advantage of providing an easier accommodation to a wide range of input light levels. The “saturation” characteristic of the image orthicon, referred to as the “knee”, is useful in limiting high light overload situations in scenes, e.g., specular reflections from glass or jewelry. These curves allow the determination of the signal level to be expected from a given type of camera tube and hence the type of processing amplifier required.

TUNGSTEN SOURCE:

11.5

The the signal-to-noise ratio associated with the photoemission or photoconductive current resulting from the image on the photosensor. In general, the limitation for vidicons results from amplifier noise. Thus, vidicons having the highest responsivity have the highest signal-to-noise ratio at a given light level.

Figure 11-18, which shows the signal-to-noise ratio of the most common type camera tubes, is for guidance purposes only because individual types within a camera tube grouping have many varieties in size, responsivities, and internal electrode spacings. In the measurement of S/N it is assumed that the amplifier

Image and Camera Tubes

191

bandwidth is 4 MHz and the input noise figure is 5 nA. However, it is to be noted that the signal current is not only dependent on the faceplate illuminance but also on the area of the active raster, with the larger-area devices providing higher signal currents. In the curves shown for the SIT and

SEC tubes, which have substantial target gain, the S/N ratio was determined by taking the amplified photoelectron noise and the amplifier noise in quadrature. The electron scanning beam of the image orthicon and image isocon is an additional source of noise, but the multiplier gain is sufficiently high so that the amplifier noise is negligible. The curves shown in Figure

11-18 for these return-beam-type camera tubes were taken with the beam setting fixed at one stop above the knee.

FACEPLATE ILLUMINANCE - LUX

Fig. 1 l-l 8 Signal-to-noise ratio characteristics of typical camera tubes.

11.6 LAG

The lag characteristic is an important consideration in selecting a camera tube for a given application, especially at low signal levels. Figure 11-19 shows the range of lag observed or calculated for the different camera-tube types as a function of faceplate illuminance.

The lag shown is the “third field” lag, i.e., the residual signal that is observed three fields (3/60th second) after the light is removed from the tube. Lag is expressed as a percentage of the original signal. For the typical vidicon, which does not have unity gamma, corrections have been made to the measurement to show the lag percentage in terms of the light level. Because the gamma is the order of 0.65, this correction lowers lag values by a substantial amount, shown in Figure 11-19. The lower corrected curve can then be directly with the linear (unity gamma) devices.

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Electro-Optics Handbook

Lag in camera tubes is associated with photoconductive and capacitive effects. Photoconductive lag occurs in certain vidicon types when charge carriers are trapped between the valence and conduction bands in states associated with impurities or imperfections. The time required for thermal excitation to occur and return the carrier to its role as a conductor depends upon the separation of the trap from the appropriate band. The time constant increases at low excitation levels because under this condition only the deeper traps are filled. Photoconductive lag occurs in photoconductive targets such as Sb2S3, PbO, CdSe, but not in Si.

FACEPLATE ILLUMINANCE - LUX

Fig. 1 I-19 Lag characteristics of typical camera tubes.

Capacitive lag occurs as a result of the finite time it takes the electron-scanning beam to remove the charge accumulated on the camera tube target. For a high-capacitance target, a longer time is required for discharge. For low target voltage, a longer time is required to discharge the target because of the exponential dependence of the beam-landing characteristic on target voltage. Thus, capacitive lag also increases as the light level decreases. The lag characteristic for the Sb2S3 photoconductive target vidicon shown in Figure 11-19 is a combination of both photoconductive and capacitive lag. The other lag characteristics shown in this figure result from capacitive lag only. Capacitive lag may be characterized by the quotient of the target capacitance and the target gain. Figure 1 l-20 presents data illustrating these characteristics which may be compared with the results of

Image and Camera Tubes 193

sensor current. Lag is also a function of target area; the smaller the area, the less the lag. The SIT tube has the lowest lag despite its relatively high target capacitance because of its higher gain and the reduced target size caused by demagnification by the image section electron optics. Data are shown only for the silicon-type vidicon where the lag is capacitive. The other types of vidicons, e.g., Sb2S3, PbO, or CdSe, have lag characteristics that are dominated by photoconductive trapping effects. Lag values larger than 20 to

30 per cent result in objectionable smearing in scenes with motion; commercial broadcast requirements are in the range of 10 per cent, or less.

Tube type

Image Orthicon

Image Isocon Glass, target-tomesh spacing,

7.5

3 2.5

SEC

Si Vidicon

KC1

Si diode array

300

4500

70

1

4

4500

SIT Si diode array 4500 1500 3

Fig. 11-20 Parameters affecting capacitive lag in typical camera tubes.

11.7 MODULATION TRANSFER FUNCTION (MTF) AND CONTRAST

TRANSFER FUNCTION (CTF) CHARACTERISTICS

Although it is preferable to measure the resolution performance of camera tubes in terms of MTF, for practical purposes, the CTF characteristicssquare-wave, black and white patterns, see Section 8-are frequently specified in data sheets. CTF and MTF values may be converted from one to the other as shown in Section 8.3.

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Electro-Optics Handbook

Fig. 11-21 Modulation transfer function (MTF) characteristics of typical camera tubes. (Based on reference 86).

Image and Camera Tubes

195

It has been shown (Reference 86) that MTF values may be closely value from about 1.l to 2.1. It is to be noted that if the line spread function for the device is gaussian in character, then n = 2. When the log-log of T(f)-’ is plotted as a function of the log of f, a straight line is obtained which permits extrapolation to other MTF values, such as the limiting resolution value (approx. 3%). Figure 11-21 shows MTF characteristics for a number of different camera tube types.

principally limited by the electron-beam characteristic and for the same size format are essentially identical. The silicon vidicon is somewhat lower in response because of the finite size of the silicon diodes and the thickness of the target, in addition to the effects of the electron beam. The MTF of a return-beam vidicon (RBV) is also shown in Figure 11-21. In this type of tube, the scanning beam is returned to a multiplier section just as in the image orthicon. When a high resolution gun and a large-format photoconductive target are used, the RBV can provide very high resolution capability. O.H.

Schade, Sr. has reported on the return beam vidicon (Reference 87), but the tube type is not generally available commercially and has only been mentioned to indicate the state of the art in high-resolution camera tube developments.

In addition to beam effects and target losses affecting MTF, some camera tube types have additional losses due to the electron-optic characteristics in the image section of the device, the finite fiber size in fiber-optic faceplates, and, in image-intensifier camera-tube combinations, the thickness and particle size of the phosphors.

11.8 LIMITATIONS TO LOW-LIGHT-LEVEL VIEWING reflected from an area the size of a single typed letter and are focused by the lens of the eye onto the retina. However, on a dark night, the number of photons per second striking the retina from the same area may be less than

100. The quantum efficiency of the eye for “white” light is estimated to be of the order of 3 per cent. Thus, in a night scene the number of detected photons from a picture element can be very small. For night viewing, the statistical variation in the number of detected photons from a picture element during an observation time may actually exceed the differences to be expected because of the variation in contrast in the scene. The fundamental

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Electro-Optics Handbook

statistical problem in picture element identification is examined first before considering the use of optical lenses and image and camera tubes to enhance recognition capability.

11.9 RECOGNITION STATISTICS

Figure 11-22 illustrates a scene composed of an array of square picture elements. One picture element, A, is assumed to have a higher luminance level than the background elements, B.

Fig. II-22 Artificial pattern related to statistical detection of elements making up a scene.

The criterion for identifying picture element A as brighter than that of the background B may be established as follows: During a time of observation, it element B. Contrast, C, may then be defined as:

AN

(1 l-l)

Therefore, l/C contrast bands have also been defined.

outside a one contrast band depends upon the width of the contrast band,

Image and Camera Tubes 197

would exceed one contrast band from the true value is 31.7 per cent. (The

To obtain a higher probability of success than that defined by lo assume that

(11-2) where k is called the “certainty coefficient”. By referring to tables of normal distribution (See Reference 88), one may tabulate the probability that a given measurement for a square is inaccurate by more than 1 contrast band.

k

1

2

3

4

5

Probability Measurement

Error Will Exceed One Contrast

Band

3.173 x 10-l

4.55 x 10

-2

2.7 x 10-3

6x 10

-5

6 x l0

-7

The selection of the certainty coefficient depends on the complexity of the picture and the degree of certainty that is required. For example, in a TV picture there may be about 200,000 picture elements displayed per frame time of l/30 second. To faithfully reproduce all elements within one contrast band, the value for k should be at least 5. However, if the approximate location of a test-pattern picture element within a scene is known, a k value of if a test pattern contains n picture elements because the average of the n elements is better determined by this factor. The same concept can be used when the detection of an object whose size and shape are known is attempted.

which corresponds to the white area A in Figure 1 l-22 but gives the density of detected photons per unit area per unit time, is introduced to equation 11-2 then

(11-3)

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Electro-Optics Handbook

t d = the dimension of the resolution element

Changing the criterion of detection to the illuminance on the scene, provides terms which is closely related to

(11-4)

Equation 11-4 indicates that the illuminance required for detection increases directly as the number of picture elements per unit area, l/d2 ; and decreases as the time of observation increases.

A different expression is often developed when the test pattern being observed consists of equal alternate bars of different contrast. In this case variances are added representing the noise in both bars. Thus,

By eliminating Nb and using the definition of C as specified by equation 1 l-l, the following equations are obtained

(11-6) and

(11-7)

Equation 1l-6 may be compared with equation 11-2. Similarly equation 11-7 may be compared with equation 11-4. The equation 11-4 corresponds more closely to a real scene, not one having equal background and signal areas.

When the background area is much larger than the signal object, the background variance term is reduced in proportion to the relative area of the background to the signal spot area and may be neglected. Because the U.S.

Air Force 1951 three-bar test pattern has a substantially greater background area than the bar pattern area, a more accurate significant general expression probably lies between equations 11-4 and 11-7.

Image and Camera Tubes

11.l0 LENS AND SENSOR LIMITATIONS

199

Although the F/number of the lens system determines the angle of view, it has no significance in the relationship between the number of photons falling on a picture element in a scene and the number of photons directed by the lens from the element to the photosensor. Only the lens diameter, D, and the lens transmission, T, are needed to specify the flux associated with a particular picture element.

Assume an object picture element is located at some distance, s, from the lens and that it is located on the lens axis and in a plane normal to the lens axis. If n photons per unit time are incident on the picture element, then the corresponding rate of arrival of photons on the sensor which forms the image element is given by the following equation.

Rate of arrival of photons = nRD2T

4 s2

(11-8) where R = the scene reflectance. A Lambertian distribution of reflected photons in the scene is assumed. The number of detected photons per picture element at the sensor in an observation time t is, therefore, given by the expression nRD2Tt

4 s2

(1 l-9) where n = the quantum efficiency of the sensor.

The expression 1 l-9 is helpful when comparing the relative advantage that image and camera tube systems have over the unaided eye in very-low-lightlevel, statistically limited viewing. Only three factors are involved in the comparison: the effective diameter of the lens, the quantum efficiency of the sensor, and the time of observation.

The time constant of the eye is often quoted as 0.2 second, but this time varies with light level and becomes longer as the light level decreases. The time constant of an image-intensifier system is a combination of the phosphor decay time and the time constant of the eye. In an image-intensifier camera-tube system, the lag of the camera tube at low signal levels must be considered. Target storage or photographic exposure techniques are often used to achieve very long integration times-providing the scene is stationary.

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Electro-Optics Handbook

It is of interest to compare the effectiveness of the unaided eye with optical lenses (telescopes, binoculars), image intensifiers and intensifier-camera tubes for low light level detection capability. The effective diameter of the dark-adapted eye is about 6 mm. For a catadioptic-type lens which is used in night vision optical devices, the T/number may be 1.5 and have a focal length of 300 mm. The effective diameter is therefore 200 mm including the transmission losses. The use of this lens affords an improvement over the unaided eye of 1100 times in the number of photons collected. From equation 1 l-4, for a given light level, the optical lens thus reduces the smallest resolvable picture element in a scene by a factor of 33 when compared with the eye alone.

In order to compare the effective quantum efficiency of the eye with that of a photosensor element used in photoemissive imaging devices, account must be taken of the different numbers of photons across the spectrum expression 11-9 and divide by the integral of n over the involved band of wavelengths. For the eye over a wavelength band of 300 nanometers, the effective quantum efficiency for “white” light is 3 per cent. See Reference

50. The 3 per cent value is calculated from Blackwell’s data for eye performance assuming that vision is statistically limited at very low light levels.

For a typical photoemissive photocathode, the extended-red multialkali type, the ratio of detected photons in the total responsivity range of the photocathode to the number of photons in the visible range of the spectrum is 13 per cent for natural night sky irradiance. See Figure 6-12. This value is not quantum efficiency in the usual sense but is weighted to compare the advantage of the photocathode sensor over that of the unaided eye. The advantage of using the multialkali photocathode with a 2OO-mm lens is an approximate factor of 1.6 x 10

4

in the number of observed photon events, or a reduction factor of 125 in picture element size when compared with the eye alone.

A low-light-level viewing system thus requires a sensitive photocathode and a large lens to collect the radiation. However, a further requirement is that a relatively noise-free gain mechanism must be provided so that picture presented to the observer is statistically limited by the photoelectron arrival rate and not by noise in the gain mechanism. For a direct-view image-intensifier system, the luminance gain must be at least 2 x 104. This gain is readily obtainable from three-stage image intensifiers and from second-generation (microchannel-plate) image tubes. In the TV camera system, a noise-free gain mechanism must be provided so that the amplified photoelectron noise in the signal exceeds that of any other noise source in the

Image and Camera Tubes

201

system, e.g., electron beam or amplifier noise. This noise condition is approached by various camera-tube image-intensifier coupled devices.

The limiting resolution of a device at low light levels can be compared with the theoretical considerations implied by equation 11-4. Limiting resolution is generally measured with a bar pattern having 100 per cent contrast. For image tubes it is usually specified in terms of line-pairs per millimeter; for camera tubes, in terms of the number of TV lines (black and white) that can be resolved in a picture height. One black and white line is equivalent to one line pair. See equation 11-4. The limiting resolution value corresponds to an

MTF of about 3 per cent at high light levels where picture noise is not a limitation. As the light level is reduced, the number of resolved lines decreases because of the obscuration caused by the noise in the picture. Limiting resolution varies approximately as the square root of the scene luminance at low light levels but is MTF limited at high light levels.

However, because the limiting resolution values are obtained using a 100 per cent contrast pattern, these values tend to give misleading information when compared to the performance capability in a real scene. With actual scene contrast values of 30 per cent, or less, the resolution is considerably reduced.

Figure 11-23 shows a limiting resolution characteristic for a fiber-optic, three-stage, electrostatistically focused image tube. The dashed line represents

Fig. 1 l-23 Limiting-resolution characteristics of a three-stage electrostatically focused image tube with fiber-optic coupling.

202 Electro-Optics Handbook

calculated values from equation 11-4 for t = 0.2 second (the integration time of the eye), C = 1, and k = 1. This resolution measurement was made with the

U.S. Air Force pattern which consists of groups of three white bars (each 5 x the width) separated by equal black spaces.

The small value of k seems to provide a good fit to the experimental data and its choice is justified because (1) the location of the minimum distinguishable pattern is quite well known from its relationship to other elements of the test pattern, and (2), the eye-brain combination uses a number of the 15 elements of the pattern in the process of decision and the value of k is reduced by the square root of this decision number.

11 .1 1 PRACTICAL DETECTION AND RECOGNITION

PARAMETERS

The probability of detection and recognition of specific objectives has been determined experimentally by the Night Vision Laboratory of the U.S. Army

Electronics Command at Fort Belvoir, Virginia. Figure 1 l-24 shows the probabilities of detection and of recognition as a function of the number of cycles of limiting resolution equivalent to the critical target dimension

(minimum height or width). From Figure 11-24 it can be seen that there is a

60 per cent possibility of recognizing a vehicle if three cycles of spatial information can be resolved (6 picture elements) in the height of the vehicle.

0 1 2

3 4 5

Fig 11-24 Probability of detection and recognition as a function of system resolution across critical target dimensions (Courtesy U.S. Night

Vision Laboratory, Fort Belvoir, VA.)

Image and Camera Tubes 203

The nomograph of Figure 1l-25 relates those parameters which influence the performance of a low-light-level image-intensifier system. The nomograph is based on the detection and recognition probability data of Figure 1l-24. The curves for the different contrast values are shifted from the 100 per cent contrast data in accordance with the theoretical concept illustrated by equation 1l-4 and the implied definition of contrast.

The shapes of the limiting resolution curves are based on the combination of tube limiting resolution at high light levels and the square root relationship

(resolution as a function of illuminance) at low light levels by the approximation:

An example of the use of the nomograph follows. Assume an illuminance of 2 first quarter on a clear night in a remote country scene) and that the object viewed reflects 10 per cent of the incident light. A line drawn from the 2 x an assumed transmission of 90 per cent, a line projected from this line of the object against the background is 30 per cent, then by extending a vertical line to the 30 per cent contrast curve, the limiting resolution is 24 line-pairs per millimeter. With this limiting resolution value, the number of picture element cycles required for recognition, the actual dimensions of the target object and the focal length of the lens, one can now determine the range at which the object may be recognized. For example, assume the object to be recognized is a vehicle whose minimum dimension is 2 meters. From the

24 lp/mm point on the vertical axis, extend a line through the 2-meter point to reference line B. Because a wide field of view is generally preferred for close-range observation over a relatively broad scene area, a 5O-mm lens was chosen. A line is next extended through the 5O-mm focal length point to intersect reference line A. For a vehicle, the N value as obtained from Figure

1l-24 is 4 cycles per critical target dimension for an 80 per cent probability of recognition. By extending the line from reference line A through the N

Image and Camera Tubes 205

point, the maximum range is established as 600 meters. If the other parameters remained the same, the range could be extended by use of a lens having a larger focal length, but this implies a larger lens diameter and a smaller field of view.

Certain camera-tube types may also be operated near the photoelectron noise limit. However, image-intensifier stages must be coupled to the input of the camera tubes to reach the lowest illuminance levels. Limiting resolution characteristics for several different types of camera tubes, for a range of contrast from 30 to 100 per cent, as functions of faceplate illuminance are shown in Figure 1l-26. Figure 11-27 shows the same characteristics for fiber-optic image-intensifier coupled camera tubes. The notation 13V indicates that a three-stage image tube is coupled to a vidicon. The dashed line at the left of the curve in both Figures 1l-26 and 11-27 is the limit to be expected for 100 per contrast and corresponds to the left side of the curve of

Figure 1l-23. The illuminance on the tube faceplates for various scene illuminances can be obtained from the nomograph of Figure 1l-25. At the very lowest levels of illuminance, and especially for scenes having high contrast, the I-SIT camera tube provides best performance. At more realistic contrast values, however, and at somewhat higher illuminance levels, the image-intensifier isocon (I-Isocon) has a higher limiting resolution capability.

Fig. 11-26 Typical resolution characteristics of selected camera tubes.

206 Electro-Optics Handbook

Figure 11-28 tabulates comparative data for several different image-intensifier camera-tube combinations when operated under starlight lighting conditions.

100

Fig. 11-2 7 Typical resolution characteristics of selected image and camera tube combinations.

References

50. Rose, A., “The Sensitivity Performance of the Human Eye on an

Absolute Scale,” J.O.S.A., Vol. 38, No. 2, Feb. 1948.

86.

Johnson, C.B., “A Method for Characterizing Electra-Optical Device

Modulation Transfer Functions,” PHOTOGRAPHIC SCIENCE AND

ENGINEERING, Vol. 14, No. 6, Nov.-Dec., 1970.

87. Schade, Sr., O-H., “Electron Optics and Signal Readout of High-

Definition Return-Beam Vidicon Camera,” RCA REVIEW, Vol. 31, No. 1,

March 1970.

88. Dixon, W.J. and Massey, F.J., INTRODUCTION TO STATISTICAL

ANALYSIS, McGraw-Hill Book Co., 1957.

89. Neuhauser, R.G., “Understanding the Vistacon,” RCA Application Note

AN-48 14.1972.

References continued on page 208.

Image and Camera Tubes 207

Output Current

Limiting Resolution

100% Contrast

Limiting Resolution

30% Contrast

Lag After 50 ms

S/N (4 MHz Bandwidth)

Output Current

Limiting Resolution

100% Contrast

Limiting Resolution

30% Contrast

Lag After 50 ms

(1) lntrascene dynamic range is here defined as the range of illuminance in a single scene such that the output signal level has a range of 5O: 1.

(2) Usable light range is the total range of illuminance which can be accommodated by variation of gain within the tube as well as by the inherent intrascene dynamic range capability.

Fig. I l-28 Typical performance data for selected camera tubes and image and camera tube combinations operated under lowlight-level conditions

208 Electro-Optics Handbook

(References continued from page 206.)

9 0 . Schade S r . ,

O.H., Resolving Power Functions and Integrals of

High-Definition Television and Photographic Cameras-A New Concept in

Image Evaluation,” RCA REVIEW, Vol. 32, No. 4, Dec. 1971.

9 1. Rodgers III, R-L., “Beam-Scanned Silicon Targets for Camera Tubes,”

IEEE INTERCON PROC., March 1973.

92. Rodgers III, R.L., “Charge-Coupled Imager for 525-Line Television,”

IEEE INTERCON PROC., March 1974.

Section

Back

2 0 9

This section provides simple formulae and definitions that are useful in understanding overall lens requirements for electro-optical systems. Also included are data on the optical properties of glass and on corner reflectors.

12.1 THIN-LENS CHARACTERISTICS AND FORMULAE

A thin lens can be described as either a converging lens or as a diverging lens which has negligible thickness compared with the object and image distances.

These lens types have relatively small apertures. The convergent, or positive, lens which is thicker at the center than at its edges, will converge a beam of collimated or parallel light rays to a real focus. The divergent, or negative, lens which is thinner at its center than at its edges will diverge a beam of collimated light. See Figure 12-l.

Focal length, f, is the image distance when the object is infinitely distant.

Lens manufacturers normally determine f using a collimated light source.

Focal length f is positive for a converging lens and negative for a diverging lens.

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Electro-Optics Handbook

CONVERGENT LENS

Fig. 12-1 Simple thin-lens types.

DIVERGENT LENS

Thin-lens formula. The relationship between the focal length and the

distances between the lens and the object and the lens and the image is given

(12-1) where

Another formulation of this equation, attributed to Newton, is

Focal length and index of refraction, n. The relationship between focal

length, f, and the index of refraction, n, is given by

(12-3) where

NOTE:

A convention of signs is observed such that both radii are considered positive if the center of curvature is to the right of the vertex (intersection of the surface of the lens with the optical axis).

Image Magnification, m is given by

Thin lenses in contact. When two thin lenses having different focal lengths are

F/number or “speed” of a lens is a measure of the angular acceptance of the

lens.

where

D = the entrance pupil diameter of the lens (assuming the lens has a circular cross section)

T/number is the effective F/number of the lens and includes the lens losses.

Thus,

= the transmittance of the lens optics

Numerical Aperture (NA). The numerical aperture, like the F/number, is a

measure of the acceptance angle of the lens. Numerical aperture is, however, more applicable to all types of lenses, especially for those having relatively large apertures.

2 1 2

where

Electra-Optics Handbook

12.2 THICK-LENS CHARACTERISTICS

Principal Planes are the surfaces formed through the intersection points

defined by extending the rays parallel to the optical axis entering the system until they intersect the backward extension of the corresponding emerging rays. See Figure 12-2.

Principal Points are the intersections of the principal planes with the optical

axis. The primary focal point and the primary principal point are those defined by rays entering the lens from the right. The secondary focal point and the secondary principal point are defined by rays entering from the left.

Focal Lengths. The effective focal length (f

eff

) for a thick lens is illustrated in

Figure 12-2; this length is the distance from the secondary principal plane to the secondary focal point. The front focal length (f fr

) is the distance between the primary principal plane and the primary focal point. The back focal length (f b

) is measured from the vertex of the last surface of the lens to the secondary focal point.

The advantage of defining the principal points is that thin lens formulae such as equations 12-1 and 12-2 may be applied to thick lenses provided the object distance is measured from the primary principal point and the image distance is measured from the secondary principal point.

12.3 LENS ABERRATIONS

Spherical Aberration: when various zones of the refracting surface focus the

incident ray bundle at different points along the optical axis.

Coma: when an object point is off-axis, and the various zones of the refracting surface magnify images by different amounts and the images formed by the various zones are displaced from the axis by various amounts.

Optics

2 1 3

SECONDARY

PRINCIPAL

OPTICAL AXIS

PRIMARY PRINCIPAL

Fig. 12-2 Thick-lens characteristics.

Astigmatism : when light rays passing through the lens in a vertical plane

focus at a different distance than light rays passing through the lens in a horizontal plane.

Field Curvature: when a plane surface normal to the optical axis is imaged by

the lens not into a plane but into a curved surface.

Distortion: when the magnification of an object line segment varies with its

distance from the optical axis of the lens. If the image of a rectangle appears with its sides curved inward, this aberration is called positive or pincushion distortion. If the sides curve outward, it is called negative or barrel distortion.

Chromatic Aberration (longitudinal): when light rays of different wavelengths

focus at different distances from the lens.

The table of Figure 12-3 indicates how the different types of aberrations vary with image height, size of aperture, and field angle.

12.4 MTF CHARACTERISTICS OF LENSES

The modulation transfer function (MTF) of a perfect, diffraction-limited circular lens is a function of the wavelength and the F/number of the lens for incoherent radiation. MTF is given by the following equation.

(12-9)

(See Reference 93).

2 1 4

Electra-Optics Handbook

Aberration

Spherical

Coma

Astigmatism

Field

Curvature

Distortion

Chromatic

(Longitudinal)

Image Height

(h)

Independent h h

2 h

2

Aperture Size

(d)

d

2 d

2

Independent

Independent h

2

Independent

Independent

Independent

Field Angie

(a)

Independent a a

2 a

2 a

3

Independent

Fig. 12-3 Relationship of lens aberrations to image height, aperture size, and field angle.

F/number of 5.6. An experimentally measured curve for an El Nikkor lens is and a nominal F/number (fully opened) of 3.5.

Lenses may be corrected to achieve various objectives; for example, low-light-level TV systems require the highest possible MTF, especially in the low range of spatial frequencies, because of the limitations imposed by the photoelectron statistics. For photographic purposes lenses are designed to provide optimum performance at high spatial frequencies somewhat at the expense of performance at the lower frequencies.

12.5 DIFFRACTION LIMITS

The image of a distant point source appears, for an ideal lens, as a central bright region (called the Airy disk) surrounded by a series of rings separated by dark rings. The central bright region theoretically contains 83.8 per cent of the total energy. The radius of the first null is given by

Optics

DIFFRACTION LIMITED (THEORETICAL)

0 50 100 150

SPATIAL FREOUENCY – CYCLES PER MILLIMETER

200 250

Fig. 12-4 MTF characteristic of a theoretical perfect lens and the measured

MTF characteristic of a practical lens.

(12-10) where the wavelength of the incident radiation

D = the diameter of the lens f = the focal length of the lens

The resolving power of the lens for viewing distant objects may be expressed in terms of the angular separation of two points which can just be discerned.

This minimum angle, a , follows from equation 12-l 0:

Practical lenses have larger, more irregular diffraction patterns and, therefore, have somewhat less resolving power.

2 1 6

Electro-Optics Handbook

12.6 ILLUMINANCE AND IRRADIANCE FORMULAE

When an optical lens is used to image a scene on a detector faceplate or on film, the faceplate illuminance may be obtained from the following equation.

E

fp

=

E

sc

R T

r

4 F

2

( 1 + m )

2

(12-12) where

E

E sc

f P

= detector faceplate or film illuminance in lx or fc

= scene illuminance in lx or fc

R = scene reflectance

T r

= lens transmission

F = F/number of the lens m = magnification from scene to detector faceplate or film

Equation 12-12 also applies if radiant units are used. In this case, E fp

and E are expressed in units of watts per square meter (W m

-2

).

sc

Equation 12-12 can also be modified by substituting the T/number for the

E f p

= ( l u x )

2 2

4 T ( 1 + m )

(1243) where

L sc

= scene luminance in nits (lm m

-2 sr

-1

)

If luminance units of footlamberts are used in equation l-2-13, then E fp

, is in

12-13 may also be used for radiant units; in this case, E square meter (W m

-2

) and L sc fp is in watts per is in watts per square meter per steradian

( W m

-2 s r

-l

) .

The power or radiant flux reaching the image plane from a distant object,

Optics

where

2 1 7

the irradiance from a distant object at the lens aperture in watts per square meter (W m

-2

)

D = the diameter of the lens aperture in meters (m)

If the distant point source luminous intensity, equation described in

14 becomes terms of radiant intensity or

(12-15) where

Note that the F/number is not used in equations the expression for photons given in equation 11-9.

12-14 and 12-15. Compare

12.7 PROPERTIES OF OPTICAL GLASSES

Figure 12-5 gives the indices of refraction as a function of wavelength for various optical glasses.

The table of Figure 12-6 relates glasses to principal spectral lines.

indices of refraction for various optical

12.8 SPECTRAL TRANSMITTANCE OF MATERIALS

Figures 12-7 and 12-8 give spectral transmittance data for materials used as optical windows.

12.9 CORNER REFLECTORS

The amount of energy which is returned toward a radiating source from a cooperating target can be greatly increased by installing a corner reflector or an array of comer reflectors on the target. These devices are capable of retroreflecting most of the radiant power they intercept even though the source is appreciably off the axis, as shown in Figure 12-9.

218 Electro-Optics Handbook

CROWN FLINT

CRO

WN

400 500 600

WAVELENGTH – nm

Fig. 12-5 Indexes of refraction as a function of wavelength for various optical glasses (Source: Optical Industries Inc., Costa Mesa, Ca,

Catalog B, Copyright 1971; used with permission).

that is retroreflected is given by

(12-16) where

E = irradiance of the incident radiation at the corner reflector

(W m

-2

)

2 2 0

Electro-Optics Handbook

100

2 3 4 5 6 7 8 9

1000

WAVELENGTH - nm

2 3 4 5 6 7 8 9

10000

Fig. 12-7 Spectral transmittance of various window materials used in the

UV-visible and near infrared.

I 5 10 15 20 25 30 35 40

WAVELENGTH – µm

1 5 1O 15 20 25 30 35 40

WAVELENGTH – µm

Fig. 12-8 Transmittance of optical materials used in infrared detection systems (Courtesy of Santa Barbara Research Center).

incidence.

ANGLE OF INCIDENCE (0)

222

Electro-Optics Handbook

specific cube comer retroreflectors; namely:

(1) the sides are squares with linear dimensions “S”

(2) the square sides of configuration (1) along its diagonal).

(3) the aperture is circular. This retroreflector is a solid section obtained by making a cylindrical cut of maximum radius

The corner reflector of types (1) and (2) can also be made of solid materials as the type (3), in which case wider angular coverage is achieved due to bending of the light on entering and leaving the solid.

the energy retroreflected. The intensity at long range is determined also by the diffraction of the retroreflected beam. The following approximate relation applies for single corner reflectors with perfectly aligned reflecting the irradiance in watts per square meter at the corner reflector (atmospheric loss is neglected):

(12-17)

The performance of an array of corner reflectors can be formulated somewhat differently from the above because the energy reflected along the center of the beam is also proportional to the number of reflectors, or equivalently, the area used by the reflectors.

Performance parameters of several commercial retroreflectors are given in

Figure 12-10, in accordance with the following explanations. The performance of a given corner reflector or a given array of corner reflectors can be defined by the ratios:

Optics

2 2 3

This relation is often expressed in photometric units as

I v

(lumens per steradian) specific intensity =

E v

(lumens per square meter) which equals specific intensity =

I (candela)

E (lux)

Equation 12-17 gives the theoretical maximum for this performance, for single corner reflectors.

In the case of arrays of comer reflectors, the amount of performance per unit of target area A utilized is of interest and is defined by

, in units of sr

-l if the same units of area are used in E and in A. A common usage, however, is to express A in square inches as in Figure 12-10 in which case the units are in mixed English photometric units, candela per foot candle per square inch (cd fc

-1 in

-2

).

When arrays are used as an extended reflecting area, it is convenient to know the gain which they have over more ordinary reflecting surfaces. Because for a perfectly reflecting plane diffuse surface of area A (Lambertian surface) and for a perfectly reflecting isotrope of area A

2 2 4

Electro-Optics Handbook

Model

Stimsonite*

FOS-21

Description

Plastic

Array

3.839

Beamwidth

Peak Peak

Specific specific

Intensity Luminana

(cd fc

-1

) (cd fc -1 in

-2

)

0.7° 50

13

Stimsonite* Plastic

FOS-3111 Array

Hutson* *

HCC-S

2½ in. dia.

single glass corner

.67

4.91

0.3°

6 arc sec

60

5.1x10

7

90

1.0x10

7

40,600 162,000

4 . 7 x 1 0

9

1 . 9 x 1 0

1 0

*Courtesy Stimsonite Division of Elastic Stop Nut Corporation of America, Chicago, Ill.

**Courtesy Hutson Corporation, Optics Division, Arlington, Texas.

Fig. 12-10 Performance characteristics of several commercial retroreflectors.

References

93. Levi, L., APPLIED OPTICS, A GUIDE TO MODERN OPTICAL SYSTEM

DESIGN, Vol. 1. John Wiley and Sons, Inc., New York, N.Y., 1968.

94. Catalog B, Optical Industries Inc., Costa Mesa, Ca., 1971.

Back

2 2 5

Section 13

Photographing E-O Displays

This section is intended to assist those desiring to photograph electro-optic displays. Pertinent information is given on sensitometry, the science of measuring the sensitivity of photographic material (film speed) as applied to the control of operations in exposing and processing photographic materials.

In addition, information is provided on film exposure definitions and units, film selection for recording cathode-ray tube images, and lens-aperture and exposure-meter settings.

13.1 SENSITOMETRY

Optical Density - The property of photographic film to absorb light (amount

of blackening on the negative) is its optical density and is calculated from

D = log 1/T (13-1)

I where D = optical density

T = transmittance value of the film

(NOTE: Transmittance is the ratio of the amount of light that an object passes to the total light that falls upon the object; l/T is defined as opacity.)

226 Electro-Optics Handbook

Figure 13-1, which is a graphical presentation of Equation 13-1, shows a typical relationship of optical density as a function of transmittance for a film negative.

E is expressed in lux and t in seconds or in the customarily used equivalent meter-candle-seconds (m cd s).

Density-Exposure Characteristic - The characteristic curve showing a typical

film response for monochrome, negative photographic film is given in Figure

13-2. In this figure, the density D of the developed film is shown as a function of the log exposure points B and C) in Figure 13-2 is the film’s gamma and indicates how the

Fig. 13-1 Relationship of density and transmittance for a film negative.

Photographing E-O Displays

227

TR

A N

S

M I

T

T A N C E LOGEXPOSURE

DENSITY= LOG 1 T

EXPOSURE (Em)-m cd s

Fig. 13-2 Typical characteristic curve for monochrome negative photographic film (Adapted from Reference 9.5, with permission).

(13-2) densities on straight line portion of plot produced by

For certain types of films, controlling gamma by varying the development time can improve the reproduction of some scenes. Generally, low-contrast scenes can be improved by increasing the development time; high contrast scenes can usually be improved by reducing the development time. These controls, however, can be used only within the limits specified for that particular film. Because different types of developers may be recommended for a particular film, gamma-time curves, such as those shown in Figure 13-3, are provided by the film manufacturers to aid in obtaining a specific gamma during development.

Average Gradient

tionship between optical density and exposure (contrast) over the non-linear portions of the film’s characteristic curve. The two points of optical density between which the calculation is made are written as subscripts of G. For example:

228

1.6

Electro-Optics Handbook

0

3

I I I I I I I

6 7 8

9 10 11 12

4 5

TIME OF DEVELOPMENT-MINUTES

Fig. 13-3 Typical curve showing film gamma as a function of development time (Adapted from Reference 96, with permission).

and results from (1) the base material of the film having some inherent density

D and (2) a spontaneous density that occurs with the development of an

Exposure Latitude - The ability of a film to reproduce a scene over a range of

several different exposure steps is called the exposure latitude and is usually expressed in terms of some number of lens stops.

The brightness range (the difference between the darkest and lightest objects in the scene) can be shifted on the characteristic curve by varying the exposure. Changing the exposure by one lens stop (a factor of 2) results in a corresponding shift of 0.3 log exposure unit along the curve. Most black-andwhite films have an exposure latitude of 1 to 2 stops underexposure to 2 to 3 stops overexposure. A typical curve having a total exposure latitude of 4 stops is shown in Figure 13-4.

Photographing E-O Displays

2 2 9

1.6

0.4

0 0.4 0.8 1.2 1.6 2.0 2.4 2.8 3.2

LOG EXPOSURE

Fig. 13-4 Typical curve of exposure latitude (Adapted from Reference 96, with permission).

Film Speed (For Photographic Negative Materials – Monochrome and.

Continuous Tone) – In order to determine the correct exposure for a specific film, it is essential that the film speed be known. Film “speed” is another way of indicating the relative sensitivity of film. In the U.S.A., the standard designation of film speed is the ASA number (see reference 97). The ASA speed

(arithmetic) is defined in relation to the characteristic curve of the film and its expected usage. Specifically, the ASA speed (S x

) is determined by the equation:

S x

= 0.8/E m

(13-4) where E m is a particular exposure in meter-candle-seconds that corresponds to the point M of Figure 13-5. The point M has been established as that point where the density is 0.10 unit above the base plus fog density (gross fog).

To minimize the effects of different development processes, a development time has been established such that the point N of Figure 13-5, which lies 1.3

log exposure units from point M in the direction of greater exposure, represents a density interval AD = 0.80 above the density at point M. Figure 13-6 gives typical values of ASA arithmetic speed.

230

Electro-Optics Handbook

Fig. 13-5 Determining the speed of photographic negative materials (Adapted from Reference 97, with permission).

Black-and-White Reversal Processing – A film that gives the characteristics

curve shown in Figure 13-7 is called a positive film, and is generally achieved by reversal processing. By this method, the negative silver image formed is destroyed with a bleach method and the remaining light-sensitive material is exposed and processed to produce a positive image. Reversal processing is often used when a positive image is desired on film. Examples are a motionpicture film when a single copy is sufficient or a black-and-white slide projection.

Speed of Reversal Color Films – For reversal color film intended for viewing

on slide projectors, the definition of speed differs from that of photographic negative materials. With regard to the use of photographic exposure meters, however, the result is quite similar.

The arithmetic speed (ASA number) (see reference 98) is computed from the formula

S x

= 8/E m

Figure 13-8 shows the density-log exposure curve for reversal color film. The value of E m for reversal color film is determined as follows:

E m

= ( E h

E s

)

½

(13-6)

Photographing E-O Displays 231

For Log

10

E m

Values

From To

American National Standard Speed

ASA

6.35-10

6.44-10 3200

6.45 6.54 2500

6.55 6.64 2000

6.65 6.74 1600

6.75 6.84 1250

6.85 6.94 1000

6.95 7.04 800

7.05 7.14 630

7.15 7.24 500

7.25 7.34 400

7.35 7.44 320

7.45 7.54 250

7.55 7.64 200

7.65 7.74 160

7.75 7.84 125

7.85 7.94 100

7.95 8.04 80

8.05 8.14 63

8.15 8.24 50

8.25 8.34 40

8.35 8.44 32

8.45 8.54 25

8.55 8.64 20

8.65 8.74 16

8.75 8.84 12

8.85 8.94

8.95 9.04

9.05 9.14

10

8

6

Fig. 13-6 ASA speed scale (Adapted from Reference 97, with permission).

232

Electro-Optics Handbook

LOG EXPOSURE

Fig. 13-7 Characteristic curve of a positive film plotted from a reversal processing (Adapted from Reference 96, with permission).

Fig. 13-8 Determining the speed of reversal color films (Adapted from

Reference 98, with permission).

Photographing E-O Displays

233

The value of E h is defined as that exposure at a point H whose density is 0.20

unit above the base plus fog density (gross fog). The value of E s is the exposure corresponding to point S of Figure 13-8. Point S is determined by drawing a line tangent to the curve and passing through point H. If the tangent to the curve occurs at a density greater than 2.0 units above the gross fog, then the point S is taken as that point on the curve where the density is 2.0

units above the gross fog.

Photographic Papers - The characteristic curves for photographic papers are the same as those for films. Gamma values for photographic papers, however, are generally higher than for films. Photographic papers are supplied in various paper-grade numbers which are related to the gamma of the characteristic curve. The higher paper-grade numbers (3, 4, 5) are intended for use with lowcontrast negatives. Conversely, the lower paper-grade numbers (0, 1) are for use with high-contrast negatives. Grade 2 paper is used with negatives having a normal range of contrasts.

13.2 FILM SELECTION FOR CATHODE-RAY TUBE RECORDING

Film and Phosphor Spectral Characteristics - The most important consideration in selecting the proper film for CRT recording is the relationship of the spectral sensitivity of the emulsion to the spectral output of the phosphor.

Because the spectral output of most phosphors is limited to a narrow spectral range, it is necessary to select a film having a spectral sensitivity that includes the spectral output of the phosphor. Figure 13-9, Parts 1 and 2, gives the characteristics of some commonly used phosphors as well as typical films recommended for recording.

CRT Exposure Index - The film speed needed to produce a useful density on the film to record the spot intensity and writing speed of the CRT is another important consideration. One system used to define film speeds for CRT recording is the CRT Exposure Index (see reference 99). This system is based on exposures in units of ergs/cm

2 rather than meter-candle-seconds. The values required to produce net densities of 0.10, 1.00, and 2.00 with a given phosphor stimulation, film, and process are expressed as the reciprocal of the exposure in ergs/cm2. The values represent the conversion of a phosphor’s radiant energy output into film density and can be used to compare speeds of various films when used with the same phosphors.

234 Electro-Optics Handbook

Photographing E-O Displays

236 Electro-Optics Handbook

13.3 PHOTOGRAPHING CATHODE-RAY TUBE IMAGES

Camera Arrangement - Figure 13-10 illustrates a typical camera arrangement for single-frame recording. The CRT should be adjusted to provide a sharp trace at an intensity that is compatible with the application. For example, moving film recordings normally require very high intensity settings. It is helpful to take trial exposures at different intensities to determine an optimum setting.

Writing Speed - This function records how fast the image of a spot on the

CRT moves across the surface of the photographic emulsion. Writing speed should be considered in CRT moving-film recordings to assure that the combination of CRT, lens aperture, magnification, and film is capable of recording the signals. For example, assume that a sine wave is displayed on the CRT in one dimension with a frequency (f) and an amplitude of A (1/2 peak to peak).

The maximum writing speed (v s

) can then be calculated as follows:

(13-7) where M = photographic magnification

V x

= film speed perpendicular to the motion of the CRT spot image.

If the film speed << speed of the image

(13-8)

To test the maximum writing speed that can be photographed with a given combination of CRT, lens aperture, magnification, and film, record a damped sine wave and compute the writing speed where part of the waveform does not record.

13.4 LENS-APERTURE AND EXPOSURE-METER-SETTING FORMULAE

Lens Aperture - The ratio of the focal length of a lens f to the diameter of the lens D is defined as the F/number of the lens, i.e., F = f/D. The F/number is a measure of the light-collecting ability of the lens. For a given scene luminance, the illuminance on the film is inversely proportional to the square of the F/number. Cameras are usually provided with a lens-stop indicator and an adjustment control for setting the lens opening. Each stop provides a change in film illuminance by a factor of 2. Thus for a lens stop, or F/number of 2.0, the illuminance is twice that of an F/number of 2.8.

Photographing E-O Displays

LIGHT SHIELD MADE .

OF BLACK PAPER OR

LIGHT GAUGE METAL

CAMER A

LENS-TO-TUBE FACE

237

Size of

CRT

Face

(inches)

Use

Close-

U p

Lens

Focus-

Scale

Setting

(feet)

Front of Lens to Tube Face

Distance

(inches)

35mm Camera and 50mm Lens (24 x 36mm format)

3 3+ plus 2+ 15 7

3

/

4

5

3+ 15 12

1

/

4

7 2-f 6 15

1

/

4

10 1+ 6 25

1

/

2

16 1+ 10 30

2

1

/

4

x 2

1

/

4

-inch Roll-Film Camera and 80mm Lens

3

5

7

10

16

3+ plus 3+

3-+ plus 2+

3+ plus 1+

2+

1+

3

1

/

2

5

3

/

4

4 7 inf 9

3

/

4

4 14

3 22

Fig. 13-10 Camera setup

for

single-frame recording (Adapted from Reference

99, with permission).

Photographing E-O Displays 239

If L is measured in footlamberts, equation 13-12 then becomes

F2= 0.27LS

t -

X

(13-13)

References

93. Levi, L., APPLIED OPTICS, A GUIDE TO MODERN OPTICAL SYSTEM

DESIGN, Vol. 1, John Wiley & Sons Inc., New York, N.Y., 1968.

95. KODAK PROFESSIONAL BLACK-AND-WHITE FILMS, Kodak Professional Data Book, F-5, 1973.

96. BASIC PHOTOGRAPHIC SENSITOMETRY WORKBOOK, Kodak Publication Z-22-ED, 2nd edition, 1971.

97. “Method for Determining Speed of Photographic Negative Materials

(Monochrome, Continuous-Tone), “AMERICAN NATIONAL STANDARD,

ANSI PH2.5 - 1972.

98. “Sensitometric Exposure and Evaluation Method for Determining Speed of Color Reversal Films for Still Photography,” AMERICAN NATIONAL

STANDARD, ANSI PH2.21 - 1972.

99. KODAK FILMS FOR CATHODE-RAY TUBE RECORDING, Kodak

Publication P-37, 1969.

100. TECHNIQUES OF PHOTO-RECORDING FROM CATHODE-RAY

TUBES, Dumont Division of Fairchild Camera and Instrument Corporation,

1964.

101. Carroll, J.S., Editor, PHOTO-LAB-INDEX, Morgan & Morgan, Inc.,

Hastings-on-Hudson, N.Y., 1966.

Back

241

Section 14

Contributors

Following is a list of people who have

made contributions to the technical

contents of this edition.

D.A. DeWolf

A.J. DiStasio

T. Doyle

R.D. Faulkner

R.W. Fitts

P.D. Huston

G.D. Kissinger

T.T. Lewis

W.D. Lindley

C.A. Meyer

A.G. Nekut

R.G. Neuhauser

R.C. Park

D.E. Persyk

G.A. Robinson

R.M. Shaffer

H .A. Weakliem

Back

243

Index

Aberration, chromatic

. . . . . . . . . . . . . . . . . . . . . . . . .

.213

Aberration, lens . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

.212

. . . . . . . . . . . . . . . . . . . . . . . . . .

.212

Aberration, spherical

Absorptance

Airy disk

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

12

Aerosol scattering . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

82

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

,214

Albedo

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

64

American national standard for letter symbols

. . . . . . . . . . . . . . 26

American national standard speed, film . . . . . . . . . . . . . . . . . .231

Angle conversion factors

. . . . . . . . . . . . . . . . . . . . . . .

23, 25

Angular threshold of eye

. . . . . . . . . . . . . . . . . . . . . . . . . 120

Anode pulse, characteristics . . . . . . . . . . . . . . . . . . . . . . .

. 168

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. 169

Fall time

Rise time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. 169

Apostilb . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

19, 20

Argon arc lamp

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

78

Array, corner reflectors . . . . . . . . . . . . . . . . . . . . . . . . .

. 222

ASA speed scale, film . . . . . . . . . . . . . . . . . . . . . . . . . .

. 231

ASA speed, film . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. 229

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. 213

Atmospheric backscatter

. . . . . . . . . . . . . . . . . . . . . . . . .

97

Atmospheric effects on sensor performance

. . . . . . . . . . . . . . . 93

Atmospheric transmittance . . . . . . . . . . . . . . . . . . . . . . . .

8 1

Factor (TA)

. . . . . . . . . . . . . . . . . . . . . . . . . . . . .

.101

In 0.4 to 4 pm region . . . . . . . . . . . . . . . . . . . . . . . . . .

87

. . . . . . . . . . . . . . . . . . . . .

91

Electro-Optics Handbook

Attenuation coefficient . . . . . . . . . . . . . . . . . . . . . . . . . .

82

Aurora light . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

67

Avalanche diodes

. . . . . . . . . . . . . . . . . . . . . . . . . . . .

165

Average gradient, film . . . . . . . . . . . . . . . . . . . . . . . . . .

227

Avogadro’s number . . . . . . . . . . . . . . . . . . . . . . . . . . . .

24

Black and white film reversal processing

. . . . . . . . . . . . . . . . . 230

Blackbody radiation

. . . . . . . . . . . . . . . . . . . . . . . . .

15, 35

Curves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

37

Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

35

References

. . . . . . . . . . . . . . . . . . . . . . . . . . . . .

42, 43

Boltzmann’s constant . . . . . . . . . . . . . . . . . . . . . . . . . . .

24

Brightness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

18

Brightness range, film . . . . . . . . . . . . . . . . . . . . . . . . . .

228

Camera arrangement for CRT image photography

. . . . . . . . . . . 237

Camera tube

173,180

..

. . 193

Lag characteristic . . . . . . . . . . . . . . . . . . . . . . . . . . .

Low-light-level performance data

. 207

Performance characteristics

. . . . . . . . . . . . . . . . . . . . .

189

Performance data . . . . . . . . . . . . . . . . . . . . . . . . . . .

207

Resolution characteristics . . . . . . . . . . . . . . . . . . . . . .

205

Tube responsivity . . . . . . . . . . . . . . . . . . . . . . . . . .

185

Signal-to-noise ratio

. . . . . . . . . . . . . . . . . . . . . . . . .

190

Trade names . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

186

Transfer characteristic . . . . . . . . . . . . . . . . . . . . . . . .

185

Transfer characteristics . . . . . . . . . . . . . . . . . . . . . . . .

190

Candela . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

l 5-20

Candle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Capacitive lag, camera tube . . . . . . . . . . . . . . . . . . . . . . .

192

Carbon arc lamp . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

78

Cathode-ray tube recording . . . . . . . . . . . . . . . . . . . . . . .

233

Cavity dumping . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

128

CCD (charge-coupled device) . . . . . . . . . . . . . . . . . . . . . .

184

Certainty coefficient . . . . . . . . . . . . . . . . . . . . . . . . . .

197

Characteristic curve, film negative

. . . . . . . . . . . . . . . . . . .

Characteristics of image tube . . . . . . . . . . . . . . . . . . . . . .

176

Characteristics of thick lens . . . . . . . . . . . . . . . . . . . . . . .

2 12

Charge-coupled device (CCD) . . . . . . . . . . . . . . . . . . . . . .

184

Chroma . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

48

Chromatic aberration . . . . . . . . . . . . . . . . . . . . . . . . . .

Chromaticity diagrams . . . . . . . . . . . . . . . . . . . . . . . .

5 1, 52

Circuit noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

165

Close-confinement lasers

. . . . . . . . . . . . . . . . . . . . . . . .

137

Coherent radiation

. . . . . . . . . . . . . . . . . . . . . . . . . . .

127

Index

Color:

And human eye

. . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

Matching

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

48

Mixture curves

. . . . . . . . . . . . . . . . . . . . . . . . . . . . .

50

Reversal film speed . . . . . . . . . . . . . . . . . . . . . . . . 230,232

Colorimetry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

48

Coma . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

..212

Commercial retroreflector characteristics . . . . . . . . . . . . . . . . . 224

Cone vision

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

Cones . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

Contrast transfer function (CTF) . . . . . . . . . . . . . . . . . . . . . 114

Contrast transfer function, camera tube

. . . . . . . . . . . . . . . . . 193

Convergent lens . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 209

Conversion factors:

For illuminance quantities

. . . . . . . . . . . . . . . . . . . . . . . 18

For luminance quantities . . . . . . . . . . . . . . . . . . . . . . . . 20

For luminous exitance quantities . . . . . . . . . . . . . . . . . . . . 19

Corner reflector array . . . . . . . . . . . . . . . . . . . . . . . . . . . 222

Corner reflectors

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217

Coupled image and camera tube resolution characteristics

. . . . . . . . 205

CRT exposure index

. . . . . . . . . . . . . . . . . . . . . . . . . .

. 233

CRT image photographing

. . . . . . . . . . . . . . . . . . . . . . . . 236

Crystalline lasers

. . . . . . . . . . . . . . . . . . . . . . . . .

CTF (contrast transfer function)

128, 129

. . . . . . . . . . . . . . . . . . . .

114

CTF, camera tube . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193

D* (specific detectivity)

Darkcurrent

Dark-adapted eye . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. 200

Dark-adapted eye response

. . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . .

. 159

147,149

. . . . . . . . . . . . . . . . . . . . . . . .

45

Density-exposure characteristic . . . . . . . . . . . . . . . . . . . . . . 226

Detection

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. 109

Parameters

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. 202

Probability

. . . . . . . . . . . . . . . . . . . . . . . . . 110, 122,202

Probability factors

Detectivity

. . . . . . . . . . . . . . . . . . . . . . . . . .

,123

. . . . . . . . . . . . . . . . . . . . . . . . . . . . .

147,150

Detector characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . 145

Detector parameters, symbols, and units

. . . . . . . . . . . . . . . . . 147

Development time, film

Diffraction limits

. 227

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214

Display interpretation

. 119

Distortion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213

Divergent lens . . . .

. 209

Double heterojunction laser

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. 138

Dye lasers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. 132

Electroluminescent diodes

Systems

. . . . . . . . . . . . . . . . . . . . . . . . 143

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. 141

246

Electro-Optics Handbook

Electromagnetic spectrum . . . . . . . . . . . . . . . . . . . . . .

13, 14

Electron charge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

24

Electrostatic-type image tube . . . . . . . . . . . . . . . . . . . . . .

. 173

Emissivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

12

EN1 (equivalent noise input) . . . . . . . . . . . . . . . . . . . . 147, 150

Equivalent luminous flux . . . . . . . . . . . . . . . . . . . . . . . .

. 147

Equivalent noise input (ENI) . . . . . . . . . . . . . . . . . . . . 147, 150

Exposure:

Index, CRT recording . . . . . . . . . . . . . . . . . . . . . . . .

. 233

Latitude, film . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. 228

Meter setting, CRT image photography

. . . . . . . . . . . . . . . . 238

Photographic . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. 226

Extinction coefficient . . . . . . . . . . . . . . . . . . . . . . . . . . .

82

Eye :

Angular threshold . . . . . . . . . . . . . . . . . . . . . . . . . .

. 120

Dark-adapted . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. 200

Quantum efficiency . . . . . . . . . . . . . . . . . . . . . . . . .

. 200

Receptors

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

45

Response . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

45

Search time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. 121

Spectral responsivity . . . . . . . . . . . . . . . . . . . . . . . . . .

46

Time constant

. . . . . . . . . . . . . . . . . . . . . . . . . . . .

. 199

F/number . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. 211

Fabray-Perot cavity . . . . . . . . . . . . . . . . . . . . . . . . . . .

,136

Fall time, anode pulse . . . . . . . . . . . . . . . . . . . . . . . . . .

. 169

False alarm rate . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. 110

Far infrared response, solid-state devices . . . . . . . . . . . . . . . . . 156

Field curvature

. . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. 213

Film:

Average gradient

. . . . . . . . . . . . . . . . . . . . . . . . . . .

. 227

Brightness range

. . . . . . . . . . . . . . . . . . . . . . . . . . .

. 228

Characteristics curve

. . . . . . . . . . . . . . . . . . . . . . . . .

. 227

Development time

. . . . . . . . . . . . . . . . . . . . . . . . . .

. 227

Exposure latitude

. . . . . . . . . . . . . . . . . . . . . . . . . . .

. 228

For CRT recording . . . . . . . . . . . . . . . . . . . . . . . . . .

. 233

Gross fog . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. 228

Negative density

. . . . . . . . . . . . . . . . . . . . . . . . . . .

. 226

Negative transmittance . . . . . . . . . . . . . . . . . . . . . . . .

. 226

Opacity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

225

Spectral characteristics . . . . . . . . . . . . . . . . . . . . . . . . 233

Speed . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. 229

Speed, ASA scale . . . . . . . . . . . . . . . . . . . . . . . . . . .

. 231

Transmittance

225

Fluorescent daylight lamp

. . . . . . . . . . . . . . . . . . . . . . . .

79

Index

247

Focal length, F

. . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . 209

Thin lens . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 210

Thicklens

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. 212

Footcandle

Footlambert

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

18

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19, 20

Formulae for thin lenses

. . . . . . . . . . . . . . . . . . . . . . . . . 209

Fovea . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . 4 5

Gain, image tube

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179

Galactic irradiance

Gamma (y)

. . . . . . . . . . . . . . . . . . . . . . . . . . . .

71

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

226

Gaslasers

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128,130

Gas-filled phototubes . . . . . . . . . . . . . . . . . . . . . . . . . . . 145

Glass lasers

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. 128

Glass properties, optical . . . . . . . . . . . . . . . . . . . . . . . . . . 217

Gross fog, film

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 228

Harmonic-generator laser

. . . . . . . . . . . . . . . . . . . . . . . . ,134

Homojunction type laser

. . . . . . . . . . . . . . . . . . . . . . . .

. 138

Horizontal visibility . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87

Horizontal-path transmittance

. . . . . . . . . . . . . . . . . . . . . . 82

Hue . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. 48, 51

Human eye response

. . . . . . . . . . . . . . . . . . . . . . . . . . . 45

Illuminance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16, 17

Illuminance formula, lens . . . . . . . . . . . . . . . . . . . . . . . . . 216

Illumination . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

Image converter tube

. . . . . . . . . . . . . . . . . . . . . . . . . . 173

Image dissector

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184

Image intensifier tube . . . . . . . . . . . . . . . . . . . . . . . . . . . 173

Image isocon

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182

Image magnification (M)

. . . . . . . . . . . . . . . . . . . . . . . . . 211

Image orthicon

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181

Image tube:

Characteristics

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 176

Electrostatic type

. . . . . . . . . . . . . . . . . . . . . . . . . .

173

Inverter design

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 176

Low-light-level performance data . . . . . . . . . . . . . . . . . . . . 207

Magnetic focus type

. . . . . . . . . . . . . . . . . . . . . . . . .

,174

Modulation transfer function (MTF) . . . . . . . . . . . . . . . . .

. 177

Output phosphor . . . . . . . . . . . . . . . . . . . . . . . . . . .

. 180

Performance data . . . . . . . . . . . . . . . . . . . . . . . . . . .

. 207

Proximity focus type . . . . . . . . . . . . . . . . . . . . . . . . .

,174

Resolution

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. 176

Spectral response . . . . . . . . . . . . . . . . . . . . . . . . . . .

,180

Wafer design

. . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. 176

248

Electro-Optics Handbook

Incident flux

. 146

Opticalglass . . . . . . . . . . . . . . . . . . . . . . . . . . . 218,219

Infrared transmittance, optical material . . . . . . . . . . . . . . . . . 220

Injection laser sources . . . . . . . . . . . . . . , . . . . . . . . . . . . 142

Inverter design image tube . . . . . . . . . . . . . . . . . . . . . . . . 176

Irradiance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

Irradiance formula, lens . . . . . . . . . . . . . . . . . . . . . . . . . . 216

JEDEC phosphor designation . . . . . . . . . . . . . . . . . . . . . . . 234

Lag, camera tube . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191

Lambert . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19, 20

Lamp sources . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72

Large optical cavity (LOC) laser . . . . . . . . . . . . . . . 137, 138, 143

Laser :

Action

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127

Safety procedures

Lasers, crystalline

128, 129

Gas

128, 130

Glass

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. 128

P-N junction . . . . . . . . . . . . . . . . . . . . . . . . . . 135

LED . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

LED sources

Lens:

135, 139, 143

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. 142

Aberration

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. 212

Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. 199

Modulation transfer function (MTF) . . . . . . . . . . . . . . . . . . 213

Power

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

,211

Requirements . . . . . . . . . . . . . . . . . . . . . . . . . . . . ,209

Resolving power

. . . . . . . . . . . . . . . . . . . . . . . . . . .

. 215

Speed . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. 211

Transmittance

. . . . . . . . . . . . . . . . . . . . . . . . . . . .

. 211

Light sources, p-n junction . . . . . . . . . . . . . . . . . . . . . . . . . 135

Light-adapted eye response . . . . . . . . . . . . . . . . . . . . . . . . 45

Light-emitting diode (LED) . . . . . . . . . . . . . . . . . . 13 5, 139, 143

Limitations to low-light-level viewing . . . . . . . . . . . . . . . . . . . 195

Limiting resolution

. . . . . . . . . . . . . . . . . . . . . . . . .

119, 201

Limits of lens diffraction

. . . . . . . . . . . . . . . . . . . . . . . . . 214

Line resolution

. . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. 120

LOC (large optical cavity) . . . . . . . . . . . . . . . . . . . . . . 137, 143

Longitudinal chromatic aberration . . . . . . . . . . . . . . . . . . .

. 213

Low-light-level performance data, image and camera tubes . . . . . . . . 207

Low-light-level image intensifier system nomograph . . . . . . . . . . . 203

Index 249

Low-light-level viewing, camera tube

. . . . . . . . . . . . . . . . . .

. 195

Lumen

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

15, 16

Luminance

. . . . . . . . . . . . . . . . . . . . . . . . . . 16, 17, 18, 48

Gain, image tube

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179

Units . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

Luminous density . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

16

Efficacy

. . . . . . . . . . . . . . . . . . . . . . . . . . . .

16, 45, 55

Efficacy calculations . . . . . . . . . . . . . . . . . . . . . . . . . . 55

Efficiency. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

16, 55

Energy

Exitance

Exitance units

. . . . . . . . . . . . . . . . . . . . . . . . . . . . .

18

Flux .................................. 16

Flux density

Intensity

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Intensity standard

.

16

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15, 16

Lunar illuminance. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .63, 64, 65

Lux . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

16, 17, 18

Magnetic focus image tube

MCP (microchannel plate)

Measurement error probability

. . . . . . . . . . . . . . . . . . . . . . . . 174

. . . . . . . . . . . . . . . . . . . . . . . 175

. . . . . . . . . . . . . . . . . . . . .

. 197

Mercury short arc lamp . . . . . . . . . . . . . . . . . . . . . . . . . . 76

Mesopic eye response . . . . . . . . . . . . . . . . . . . . . . . . . . .

46

Metric system units. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Prefixes and symbols

23, 26

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

33

Microchannel plate (MCP)

MIE scattering

. . . . . . . . . . . . . . . . . . . . . . . . 175

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

82

Mode locking

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Modulation transfer analyzer

. 128

. . . . . . . . . . . . . . . . . . . . . . 177

Modulation transfer function . . . . . . . . . . . . . . . . . . . . . . . 114

Camera tube

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193

Image tube. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177

Lens

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213

Moon illuminance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

63

MTF . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . 114

Camera tube

. . . . . . . . . . . . . . . . . . . . . . . . . . . . .

193

. Characteristic of lens . . . . . . . . . . . . . . . . . . . . . . . . . . 215

Degradation by image motion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117

Image tube. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . 177

Lens. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213

Natural illuminance levels . . . . . . . . . . . . . . . . . . . . .

72, 74, 75

Natural scene illuminance . . . . . . . . . . . . . . . . . . . . . . . . .

70

250

Electro-Optics Handbook

Near-infrared spectral response for photoemissive devices

....... .151

NEP (noise equivalent power) . . . . . . . . . . . . . . . . . . . . . .

.150

Night sky irradiance . . . . . . . . . . . . . . . . . . . . . . . .

71,72,73

NIT

................................ 16,19,20

Noise

............................. 109,147,160

Current ................................ .150

Equivalent power ......................... 147,150

Nomograph for low-light level image intensifier system ......... .203

Numerical aperture (NA)

. . . . . . . . . . . . . . . . . . . . . . . .

.211

Opacity of film

............................. 225

Optical density, film

.......................... .225

Optical glass index of refraction

.................. 218, 219

Optical glass properties

......................... .2 17

Optical material infrared transmittance

................. .220

Optics ...................................209

Output phosphor, image tube . . . . . . . . . . . . . . . . . . . . . .

.180

Ozone absorption ............................. 82

P-N junction lasers

........................... .135

P-N junction light sources . . . . . . . . . . . . . . . . . . . . . . . .

.135

Parametric down-conversion

. . . . . . . . . . . . . . . . . . . . . .

.133

Performance characteristics of camera tubes

.............. .189

Performance data, camera and image tubes ............... .207

Permittivity of free space

......................... 24

Phosphor designations, JEDEC

..................... .234

Phosphor spectral characteristics

.................... .233

Photocathode cooling .......................... .158

Photocathode responsivity . . . . . . . . . . . . . . . . . . . . . . . .

.171

Photoconductive detectors

....................... .145

Photoconductive lag, camera tube

................... .192

Photodetector .............................. 145

Relationships and definitions ..................... .146

Spectral response ........................... .151

Time characteristics

......................... .167

Time response characteristics ..................... .168

With internal amplification .................... 164, 165

Photodiode noise

............................ .160

Photoemissive devices .......................... .145

Temperature effects

................

155

Photoemitter characteristics, heat; infrared-visible

............ .157

Photoemitter characteristics, visible ................... 156

Photographic exposure

......................... .226

Photographic paper . . . . . . . . . . . . . . . . . . . . . . . . . . .

,233

Photographing CRT images . . . . . . . . . . . . . . . . . . . . . . .

. 236

Electro-optical displays . . . . . . . . . . . . . . . . . . . . . . . .

. 225

Photometric quantities . . . . . . . . . . . . . . . . . . . . . . . .

. 9, 15

Photometry units . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

26

Photomultiplier

. . . . . . . . . . . . . . . . . . . . . . . .

145,146, 164

Time response characteristics . . . . . . . . . . . . . . . . . . . . .

167

Photopic eye response . . . . . . . . . . . . . . . . . . . . . . . . . .

45

Photopic vision

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

53

Photovoltaic detectors

. . . . . . . . . . . . . . . . . . . . . . . . . . 145

Physical constants . . . . . . . . . . . . . . . . . . . . . . . . . . .

23, 24

Planck’s constant

. . . . . . . . . . . . . . . . . . . . . . . . . . . . .

24

Planck’s equation for spectral radiant exitance

. . . . . . . . . . . . . . 35

Planetary spectral irradiance . . . . . . . . . . . . . . . . . . . . . . .

68

Principal planes, thick lens . . . . . . . . . . . . . . . . . . . . . . . . 212

Principal points, thick lens . . . . . . . . . . . . . . . . . . . . . . . . 212

Probability of detection . . . . . . . . . . . . . . . . . . . . . . . 110, 202

Probability of recognition . . . . . . . . . . . . . . . . . . . . . . . . . 202

Properties of optical glasses . . . . . . . . . . . . . . . . . . . . . . . 217

Proximity focus image tube . . . . . . . . . . . . . . . . . . . . . . . . 174

Pulse counting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166

Pulse detection in quantum noise . . . . . . . . . . . . . . . . . . . .

. 113

Pulse detection in white noise . . . . . . . . . . . . . . . . . . . . . .

. 109

Quantum efficiency . . . . . . . . . . . . . . . . . . . . . . . . . 147, 148

Quantum efficiency of eye

Quantum noise

. . . . . . . . . . . . . . . . . . . . . . . . 200

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109

Radiance

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

Radiant density . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

Emittance

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

Energy

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

Exitance

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

Flux . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . 1 0

Intensity

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

Radiation conversion chart

. . . . . . . . . . . . . . . . . . . . . . . . . 13

Equation constants . . . . . . . . . . . . . . . . . . . . . . . . . . .

37

Sources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

Radiometric quantities

. . . . . . . . . . . . . . . . . . . . . . . . . 9, 12

Radiometry units . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

Rayleigh scattering

. . . . . . . . . . . . . . . . . . . . . . . . . . . . 82

Receptors of the human eye

. . . . . . . . . . . . . . . . . . . . . . . 45

Recognition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109

Parameters

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202

Probability

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202

Statistics

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197

Electro-Optics Handbook

Reflectance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

12

Relationship between quanta and radiant flux units

. . . . . . . . . . . 147

Relative spectral luminous efficiency . . . . . . . . . . . . . . . . . . .

54

Resolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109

Resolution characteristics, camera tubes . . . . . . . . . . . . . . . . . 205

Image tubes and camera tubes . . . . . . . . . . . . . . . . . . . .

. 205

Image tubes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. 176

Resolving power of lens . . . . . . . . . . . . . . . . . . . . . . . . .

. 215

Responsivity . . . . . . . . . . . . . . . . . . . . . . . . . . . .

147,148

Camera tube . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. 185

Retinal receptors . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

45

Retroreflector characteristics, commercial . . . . . . . . . . . . . . . . 224

Retroreflectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. 217

Reversal processing, black and white film . . . . . . . . . . . . . . . . . 230

Rise time, anode pulse . . . . . . . . . . . . . . . . . . . . . . . . .

. 169

Rod vision . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

45

Rods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 5

S/N (signal-to-noise ratio) . . . . . . . . . . . . . . . . . . . . . . . . . 150

S/N camera tube

. . . . . . . . . . . . . . . . . . . . . . . . . . . .

. 190

Saturation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

48, 51

Scotopic vision . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

Scotopic eye response . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

SEC camera tube

. . . . . . . . . . . . . . . . . . . . . . . . . . . .

. 183

Second generation image tube . . . . . . . . . . . . . . . . . . . . . 175

Second harmonic generation . . 133

Second radiation constant (hc/k) . . . . . . . . . . . . . . . . . . . . . . 24

Secondary electron conduction camera tube . . . . . . . . . . . . . . 183

Sensitometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 225

Sensor limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199

SH-CC laser (single heterojunction, close confined) . . . . . . . . . 137, 143

SI units

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

Signal current . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148

Signal response . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147

Signal-to-noise ratio . . . . . . . . . . . . . . . . . . . . . . . . . 147, 150

Camera tube . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 190

Silicon intensifier target camera tube . . . . . . . . . . . . . . . . . . . 183

Silicon photovoltaic cells

. . . . . . . . . . . . . . . . . . . . . . . . . 146

Sine-wave spatial frequency amplitude response . . . . . . . . . . . . . 114

Single-heterojunction close-confined (SH-CC) . . . . . . . . . . . 138, 143

SIT camera tube . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183

Sky illuminance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68

Light spectral distribution . . . . . . . . . . . . . . . . . . . . . . . 7 1

Luminance

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70

Solar illuminance

. . . . . . . . . . . . . . . . . . . . . . . . . . .

61, 63

Solar irradiance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

6 1

Index

253

Electro-Optics Handbook

Speed: (Continued)

Film . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 229

Lens

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. 211

Light . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

24

Spherical aberration . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212

Square-wave spatial frequency amplitude response

. . . . . . . . . . . . 114

SS devices, visible and near-infrared spectral response . . . . . . . . . . 155

Standard color mixture curves . . . . . . . . . . . . . . . . . . . . 50, 51

Standard unit symbols . . . . . . . . . . . . . . . . . . . . . . . . . . 26

Star illuminance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

Stefan-Boltzmann constant . . . . . . . . . . . . . . . . . . . . . . . . 24

Stellar illuminance . . . . . . . . . . . . . . . . . . . . . . . . . . 65, 66

Stellar spectral irradiance . . . . . . . . . . . . . . . . . . . . . . . 67, 69

Stilb . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Sun’s irradiance

19, 20

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

61

Sun’s spectral radiance . . . . . . . . . . . . . . . . . . . . . . . . . . 62

Symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

23

T/number

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

211

Talbot . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

16

Target detection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121

Detection/recognition model . . . . . . . . . . . . . . . . . . . . . . 121

Recognition . 121

. . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Television camera tube . . . . . . . . . . . . . . . . . . . . . . . . . . 180

Thermal noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. 166

Thick-lens characteristics

. . . . . . . . . . . . . . . . . . . . . . . . . 212

Thin-lens characteristics . . . . . . . . . . . . . . . . . . . . . . . . . 209

Formulae . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. 209, 210

Types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. 210

Thin lenses in contact . . . . . . . . . . . . . . . . . . . . . . . . . . . 211

Threshold detection process . . . . . . . . . . . . . . . . . . . . . . 110

Threshold of human eye response . . . . . . . . . . . . . . . . . . . . . 46

Time constant of eye

. . . . . . . . . . . . . . . . . . . . . . . . . . 199

Time response characteristics, photomultiplier . . . . . . . . . . . . . 167

Time response characteristics, solid-state photodetector . . . . . . . . . 168

Trade names, camera tubes

. . . . . . . . . . . . . . . . . . . . . . . . 186

Transfer characteristic camera tube . . . . . . . . . . . . . . . . 185, 190

Transferance (T) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94

. . . . . . . . . . . . . . . . . . . . . . . . . .101

Transmittance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

12

Film

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

225

Optical material, infrared . . . . . . . . . . . . . . . . . . . . . . . . 220

Through gaseous atmosphere . . . . . . . . . . . . . . . . . . . . . . 81

Trichromatic response theory of human eye . . . . . . . . . . . . . . . 47

Tungsten lamp

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

78

Standard . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

Index

TV camera tube . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

180

Typical electroluminescent systems . . . . . . . . . . . . . . . . . . .

. 141

Typical lamp parameters . . . . . . . . . . . . . . . . . . . . . . . . .

76

UV-visible photoemitter characteristics . . . . . . . . . . . . . . . . .

. 155

UV-visible spectral response for photoemissive devices

. . . . . . . . . . 151

Vacuum photodiodes . . . . . . . . . . . . . . . . . . . . . . . . . .

. 145

Vidicon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

180

Visible and near-infrared response, solid-state devices . . . . . . . . . . . 155

Visible light spectral response for photoemissive devices

. . . . . . . . . 151

Visual search time . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. 121

Wafer-design image tube

. . . . . . . . . . . . . . . . . . . . . . . .

. 176

Wavelength

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

10

Wavelength of maximum spectral power

. . . . . . . . . . . . . . . . . 36

White noise

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. 109

Wien’s displacement law

. . . . . . . . . . . . . . . . . . . . . . . . .

36

Window material spectral transmittance

. . . . . . . . . . . . . . 2 17, 220

Xenon short arc lamp . . . . . . . . . . . . . . . . . . . . . . . . . . . 77

Zirconium concentrated-arc lamp . . . . . . . . . . . . . . . . . . . . .

77

Zodiacal irradiance

. . . . . . . . . . . . . . . . . . . . . . . . . . . .

7 1

Zodiacal light . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

67

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